diff --git a/yazi-actor/src/cmp/trigger.rs b/yazi-actor/src/cmp/trigger.rs
index d2e715ca..29f435b5 100644
--- a/yazi-actor/src/cmp/trigger.rs
+++ b/yazi-actor/src/cmp/trigger.rs
@@ -115,12 +115,12 @@ mod tests {
 	fn test_split() {
 		yazi_fs::init();
 		compare("foo", "", "foo");
-		compare("foo\\", "foo\\", "");
-		compare("foo\\bar", "foo\\", "bar");
-		compare("foo\\bar\\", "foo\\bar\\", "");
-		compare("C:\\", "C:\\", "");
-		compare("C:\\foo", "C:\\", "foo");
-		compare("C:\\foo\\", "C:\\foo\\", "");
-		compare("C:\\foo\\bar", "C:\\foo\\", "bar");
+		compare(r"foo\", r"foo\", "");
+		compare(r"foo\bar", r"foo\", "bar");
+		compare(r"foo\bar\", r"foo\bar\", "");
+		compare(r"C:\", r"C:\", "");
+		compare(r"C:\foo", r"C:\", "foo");
+		compare(r"C:\foo\", r"C:\foo\", "");
+		compare(r"C:\foo\bar", r"C:\foo\", "bar");
 	}
 }
diff --git a/yazi-actor/src/lives/file.rs b/yazi-actor/src/lives/file.rs
index 2de0a85b..11dce848 100644
--- a/yazi-actor/src/lives/file.rs
+++ b/yazi-actor/src/lives/file.rs
@@ -121,7 +121,7 @@ impl UserData for File {
 				_ => 0u8,
 			})
 		});
-		methods.add_method("is_selected", |_, me, ()| Ok(me.tab.selected.contains_key(&me.url)));
+		methods.add_method("is_selected", |_, me, ()| Ok(me.tab.selected.contains(&me.url)));
 		methods.add_method("found", |lua, me, ()| {
 			lua.named_registry_value::<AnyUserData>("cx")?.borrow_scoped(|core: &yazi_core::Core| {
 				let Some(finder) = &core.active().finder else {
diff --git a/yazi-actor/src/lives/selected.rs b/yazi-actor/src/lives/selected.rs
index dcab02b3..dd513b33 100644
--- a/yazi-actor/src/lives/selected.rs
+++ b/yazi-actor/src/lives/selected.rs
@@ -1,4 +1,3 @@
-use indexmap::IndexMap;
 use mlua::AnyUserData;
 
 use super::Lives;
@@ -9,11 +8,11 @@ pub(super) struct Selected;
 
 impl Selected {
 	#[inline]
-	pub(super) fn make(inner: &IndexMap<yazi_shared::url::Url, u64>) -> mlua::Result<AnyUserData> {
+	pub(super) fn make(inner: &yazi_core::tab::Selected) -> mlua::Result<AnyUserData> {
 		let inner = PtrCell::from(inner);
 
 		Lives::scoped_userdata(yazi_binding::Iter::new(
-			inner.as_static().keys().cloned().map(yazi_binding::Url::new),
+			inner.as_static().values().cloned().map(yazi_binding::Url::new),
 			Some(inner.len()),
 		))
 	}
diff --git a/yazi-actor/src/mgr/copy.rs b/yazi-actor/src/mgr/copy.rs
index d615d0f2..573aa94f 100644
--- a/yazi-actor/src/mgr/copy.rs
+++ b/yazi-actor/src/mgr/copy.rs
@@ -1,5 +1,4 @@
-// FIXME: VFS
-use std::{ffi::OsString, path::Path};
+use std::ffi::OsString;
 
 use anyhow::{Result, bail};
 use yazi_macro::{act, succ};
@@ -28,13 +27,24 @@ impl Actor for Copy {
 		.peekable();
 
 		while let Some(u) = it.next() {
-			s.push(match opt.r#type.as_ref() {
-				"path" => opt.separator.transform(u),
-				"dirname" => opt.separator.transform(u.parent().unwrap_or(Path::new(""))),
-				"filename" => opt.separator.transform(u.name()),
-				"name_without_ext" => opt.separator.transform(u.file_stem().unwrap_or_default()),
+			match opt.r#type.as_ref() {
+				// TODO: rename to "url"
+				"path" => {
+					s.push(opt.separator.transform(&u.os_str()));
+				}
+				"dirname" => {
+					if let Some(p) = u.parent_url() {
+						s.push(opt.separator.transform(&p.os_str()));
+					}
+				}
+				"filename" => {
+					s.push(opt.separator.transform(u.name()));
+				}
+				"name_without_ext" => {
+					s.push(opt.separator.transform(u.file_stem().unwrap_or_default()));
+				}
 				_ => bail!("Unknown copy type: {}", opt.r#type),
-			});
+			};
 			if it.peek().is_some() {
 				s.push("\n");
 			}
@@ -42,7 +52,7 @@ impl Actor for Copy {
 
 		// Copy the CWD path regardless even if the directory is empty
 		if s.is_empty() && opt.r#type == "dirname" {
-			s.push(opt.separator.transform(cx.cwd()));
+			s.push(opt.separator.transform(&cx.cwd().os_str()));
 		}
 
 		futures::executor::block_on(CLIPBOARD.set(s));
diff --git a/yazi-actor/src/mgr/toggle_all.rs b/yazi-actor/src/mgr/toggle_all.rs
index f79252c5..ec2d5101 100644
--- a/yazi-actor/src/mgr/toggle_all.rs
+++ b/yazi-actor/src/mgr/toggle_all.rs
@@ -23,8 +23,8 @@ impl Actor for ToggleAll {
 			Some(true) => Right((vec![], opt.urls)),
 			Some(false) if opt.urls.is_empty() => Left((it.collect(), vec![])),
 			Some(false) => Right((opt.urls, vec![])),
-			None if opt.urls.is_empty() => Left(it.partition(|&u| tab.selected.contains_key(u))),
-			None => Right(opt.urls.into_iter().partition(|u| tab.selected.contains_key(u))),
+			None if opt.urls.is_empty() => Left(it.partition(|&u| tab.selected.contains(u))),
+			None => Right(opt.urls.into_iter().partition(|u| tab.selected.contains(u))),
 		};
 
 		let warn = match either {
diff --git a/yazi-actor/src/mgr/yank.rs b/yazi-actor/src/mgr/yank.rs
index 2a96ec7f..a68368b8 100644
--- a/yazi-actor/src/mgr/yank.rs
+++ b/yazi-actor/src/mgr/yank.rs
@@ -2,7 +2,7 @@ use anyhow::Result;
 use yazi_core::mgr::Yanked;
 use yazi_macro::{act, render};
 use yazi_parser::mgr::YankOpt;
-use yazi_shared::event::Data;
+use yazi_shared::{event::Data, url::CovUrl};
 
 use crate::{Actor, Ctx};
 
@@ -16,7 +16,8 @@ impl Actor for Yank {
 	fn act(cx: &mut Ctx, opt: Self::Options) -> Result<Data> {
 		act!(mgr:escape_visual, cx)?;
 
-		cx.mgr.yanked = Yanked::new(opt.cut, cx.tab().selected_or_hovered().cloned().collect());
+		cx.mgr.yanked =
+			Yanked::new(opt.cut, cx.tab().selected_or_hovered().cloned().map(CovUrl).collect());
 		render!(cx.mgr.yanked.catchup_revision(true));
 
 		act!(mgr:escape_select, cx)
diff --git a/yazi-binding/src/url.rs b/yazi-binding/src/url.rs
index 91261abb..95a82ad6 100644
--- a/yazi-binding/src/url.rs
+++ b/yazi-binding/src/url.rs
@@ -1,7 +1,7 @@
 use std::{borrow::Cow, ops::Deref};
 
 use mlua::{AnyUserData, ExternalError, FromLua, Lua, MetaMethod, UserData, UserDataFields, UserDataMethods, UserDataRef, Value};
-use yazi_shared::url::Scheme;
+use yazi_shared::url::{CovUrl, Scheme};
 
 use crate::{Urn, cached_field};
 
@@ -41,6 +41,10 @@ impl<'a> From<&'a Url> for Cow<'a, yazi_shared::url::Url> {
 	fn from(value: &'a Url) -> Self { Cow::Borrowed(&value.inner) }
 }
 
+impl From<Url> for yazi_shared::url::CovUrl {
+	fn from(value: Url) -> Self { CovUrl(value.inner) }
+}
+
 impl TryFrom<&[u8]> for Url {
 	type Error = mlua::Error;
 
@@ -159,10 +163,10 @@ impl UserData for Url {
 
 		methods.add_meta_method(MetaMethod::Eq, |_, me, other: UrlRef| Ok(me.inner == other.inner));
 		methods.add_meta_method(MetaMethod::ToString, |lua, me, ()| {
-			lua.create_string(me.as_os_str().as_encoded_bytes())
+			lua.create_string(me.os_str().as_encoded_bytes())
 		});
 		methods.add_meta_method(MetaMethod::Concat, |lua, lhs, rhs: mlua::String| {
-			lua.create_string([lhs.as_os_str().as_encoded_bytes(), &rhs.as_bytes()].concat())
+			lua.create_string([lhs.os_str().as_encoded_bytes(), &rhs.as_bytes()].concat())
 		});
 	}
 }
diff --git a/yazi-core/src/mgr/yanked.rs b/yazi-core/src/mgr/yanked.rs
index e585ceff..e585419b 100644
--- a/yazi-core/src/mgr/yanked.rs
+++ b/yazi-core/src/mgr/yanked.rs
@@ -3,28 +3,28 @@ use std::{collections::HashSet, ops::Deref};
 use yazi_dds::Pubsub;
 use yazi_fs::FilesOp;
 use yazi_macro::err;
-use yazi_shared::url::Url;
+use yazi_shared::url::{CovUrl, Url};
 
 #[derive(Debug, Default)]
 pub struct Yanked {
 	pub cut: bool,
-	urls:    HashSet<Url>,
+	urls:    HashSet<CovUrl>,
 
 	version:  u64,
 	revision: u64,
 }
 
 impl Deref for Yanked {
-	type Target = HashSet<Url>;
+	type Target = HashSet<CovUrl>;
 
 	fn deref(&self) -> &Self::Target { &self.urls }
 }
 
 impl Yanked {
-	pub fn new(cut: bool, urls: HashSet<Url>) -> Self { Self { cut, urls, ..Default::default() } }
+	pub fn new(cut: bool, urls: HashSet<CovUrl>) -> Self { Self { cut, urls, ..Default::default() } }
 
 	pub fn remove(&mut self, url: &Url) {
-		if self.urls.remove(url) {
+		if self.urls.remove(CovUrl::new(url)) {
 			self.revision += 1;
 		}
 	}
@@ -38,11 +38,15 @@ impl Yanked {
 		self.revision += 1;
 	}
 
+	#[inline]
+	pub fn contains(&self, url: impl AsRef<Url>) -> bool { self.urls.contains(CovUrl::new(&url)) }
+
 	pub fn contains_in(&self, dir: &Url) -> bool {
 		self.urls.iter().any(|u| {
 			let mut it = u.components();
-			// FIXME
-			it.next_back().is_some() && it == dir.components() && u.parent_url().as_ref() == Some(dir)
+			it.next_back().is_some()
+				&& it.covariant(&dir.components())
+				&& u.parent_url().is_some_and(|p| p == *dir)
 		})
 	}
 
@@ -56,7 +60,7 @@ impl Yanked {
 
 		if !addition.is_empty() {
 			let old = self.urls.len();
-			self.urls.extend(addition);
+			self.urls.extend(addition.into_iter().map(CovUrl));
 			self.revision += (old != self.urls.len()) as u64;
 		}
 	}
diff --git a/yazi-core/src/tab/selected.rs b/yazi-core/src/tab/selected.rs
index 769e626f..3a0dc99f 100644
--- a/yazi-core/src/tab/selected.rs
+++ b/yazi-core/src/tab/selected.rs
@@ -2,21 +2,29 @@ use std::{collections::HashMap, ops::Deref};
 
 use indexmap::IndexMap;
 use yazi_fs::FilesOp;
-use yazi_shared::{timestamp_us, url::Url};
+use yazi_shared::{timestamp_us, url::{CovUrl, Url}};
 
 #[derive(Default)]
 pub struct Selected {
-	inner:   IndexMap<Url, u64>,
-	parents: HashMap<Url, usize>,
-}
-
-impl Deref for Selected {
-	type Target = IndexMap<Url, u64>;
-
-	fn deref(&self) -> &Self::Target { &self.inner }
+	inner:   IndexMap<CovUrl, u64>,
+	parents: HashMap<CovUrl, usize>,
 }
 
 impl Selected {
+	#[inline]
+	pub fn len(&self) -> usize { self.inner.len() }
+
+	#[inline]
+	pub fn is_empty(&self) -> bool { self.inner.is_empty() }
+
+	#[inline]
+	pub fn values(&self) -> impl Iterator<Item = &Url> { self.inner.keys().map(Deref::deref) }
+
+	#[inline]
+	pub fn contains(&self, url: impl AsRef<Url>) -> bool {
+		self.inner.contains_key(CovUrl::new(&url))
+	}
+
 	#[inline]
 	pub fn add(&mut self, url: &Url) -> bool { self.add_same(&[url]) == 1 }
 
@@ -33,7 +41,7 @@ impl Selected {
 	fn add_same(&mut self, urls: &[impl AsRef<Url>]) -> usize {
 		// If it has appeared as a parent
 		let urls: Vec<_> =
-			urls.iter().map(|u| u.as_ref()).filter(|&u| !self.parents.contains_key(u)).collect();
+			urls.iter().map(CovUrl::new).filter(|&u| !self.parents.contains_key(u)).collect();
 		if urls.is_empty() {
 			return 0;
 		}
@@ -79,12 +87,12 @@ impl Selected {
 	}
 
 	fn remove_same(&mut self, urls: &[impl AsRef<Url>]) -> usize {
-		let count = urls.iter().filter_map(|u| self.inner.swap_remove(u.as_ref())).count();
+		let count = urls.iter().filter_map(|u| self.inner.swap_remove(CovUrl::new(u))).count();
 		if count == 0 {
 			return 0;
 		}
 
-		let mut parent = urls[0].as_ref().parent_url();
+		let mut parent = CovUrl::new(&urls[0]).parent_url();
 		while let Some(u) = parent {
 			let n = self.parents.get_mut(&u).unwrap();
 
@@ -104,7 +112,7 @@ impl Selected {
 	}
 
 	pub fn apply_op(&mut self, op: &FilesOp) {
-		let (removal, addition) = op.diff_recoverable(|u| self.contains_key(u));
+		let (removal, addition) = op.diff_recoverable(|u| self.contains(u));
 		if !removal.is_empty() {
 			self.remove_many(&removal);
 		}
diff --git a/yazi-core/src/tab/tab.rs b/yazi-core/src/tab/tab.rs
index 63ea995b..9d4af76b 100644
--- a/yazi-core/src/tab/tab.rs
+++ b/yazi-core/src/tab/tab.rs
@@ -89,7 +89,7 @@ impl Tab {
 		if self.selected.is_empty() {
 			Box::new(self.hovered().map(|h| &h.url).into_iter())
 		} else {
-			Box::new(self.selected.keys())
+			Box::new(self.selected.values())
 		}
 	}
 
@@ -98,7 +98,7 @@ impl Tab {
 		if self.selected.is_empty() {
 			Box::new([&h.url, &h.url].into_iter())
 		} else {
-			Box::new([&h.url].into_iter().chain(self.selected.keys()))
+			Box::new([&h.url].into_iter().chain(self.selected.values()))
 		}
 	}
 
diff --git a/yazi-core/src/tasks/file.rs b/yazi-core/src/tasks/file.rs
index 65bff641..27441aad 100644
--- a/yazi-core/src/tasks/file.rs
+++ b/yazi-core/src/tasks/file.rs
@@ -1,51 +1,51 @@
 use std::collections::HashSet;
 
 use tracing::debug;
-use yazi_shared::url::Url;
+use yazi_shared::url::{CovUrl, Url};
 
 use super::Tasks;
 
 impl Tasks {
-	pub fn file_cut(&self, src: &[&Url], dest: &Url, force: bool) {
+	pub fn file_cut(&self, src: &[&CovUrl], dest: &Url, force: bool) {
 		for &u in src {
 			let to = dest.join(u.file_name().unwrap());
 			if force && *u == to {
 				debug!("file_cut: same file, skipping {:?}", to);
 			} else {
-				self.scheduler.file_cut(u.clone(), to, force);
+				self.scheduler.file_cut(u.0.clone(), to, force);
 			}
 		}
 	}
 
-	pub fn file_copy(&self, src: &[&Url], dest: &Url, force: bool, follow: bool) {
+	pub fn file_copy(&self, src: &[&CovUrl], dest: &Url, force: bool, follow: bool) {
 		for &u in src {
 			let to = dest.join(u.file_name().unwrap());
 			if force && *u == to {
 				debug!("file_copy: same file, skipping {:?}", to);
 			} else {
-				self.scheduler.file_copy(u.clone(), to, force, follow);
+				self.scheduler.file_copy(u.0.clone(), to, force, follow);
 			}
 		}
 	}
 
-	pub fn file_link(&self, src: &HashSet<Url>, dest: &Url, relative: bool, force: bool) {
+	pub fn file_link(&self, src: &HashSet<CovUrl>, dest: &Url, relative: bool, force: bool) {
 		for u in src {
 			let to = dest.join(u.file_name().unwrap());
 			if force && *u == to {
 				debug!("file_link: same file, skipping {:?}", to);
 			} else {
-				self.scheduler.file_link(u.clone(), to, relative, force);
+				self.scheduler.file_link(u.0.clone(), to, relative, force);
 			}
 		}
 	}
 
-	pub fn file_hardlink(&self, src: &HashSet<Url>, dest: &Url, force: bool, follow: bool) {
+	pub fn file_hardlink(&self, src: &HashSet<CovUrl>, dest: &Url, force: bool, follow: bool) {
 		for u in src {
 			let to = dest.join(u.file_name().unwrap());
 			if force && *u == to {
 				debug!("file_hardlink: same file, skipping {:?}", to);
 			} else {
-				self.scheduler.file_hardlink(u.clone(), to, force, follow);
+				self.scheduler.file_hardlink(u.0.clone(), to, force, follow);
 			}
 		}
 	}
diff --git a/yazi-dds/src/body/yank.rs b/yazi-dds/src/body/yank.rs
index 3f1f443e..245a394e 100644
--- a/yazi-dds/src/body/yank.rs
+++ b/yazi-dds/src/body/yank.rs
@@ -3,7 +3,7 @@ use std::{borrow::Cow, collections::HashSet};
 use mlua::{IntoLua, Lua, Value};
 use serde::{Deserialize, Serialize};
 use yazi_parser::mgr::UpdateYankedOpt;
-use yazi_shared::url::Url;
+use yazi_shared::url::CovUrl;
 
 use super::Body;
 
@@ -11,13 +11,13 @@ use super::Body;
 pub struct BodyYank<'a>(UpdateYankedOpt<'a>);
 
 impl<'a> BodyYank<'a> {
-	pub fn borrowed(cut: bool, urls: &'a HashSet<Url>) -> Body<'a> {
+	pub fn borrowed(cut: bool, urls: &'a HashSet<CovUrl>) -> Body<'a> {
 		Self(UpdateYankedOpt { cut, urls: Cow::Borrowed(urls) }).into()
 	}
 }
 
 impl BodyYank<'static> {
-	pub fn owned(cut: bool, _: &HashSet<Url>) -> Body<'static> {
+	pub fn owned(cut: bool, _: &HashSet<CovUrl>) -> Body<'static> {
 		Self(UpdateYankedOpt { cut, urls: Default::default() }).into()
 	}
 }
diff --git a/yazi-dds/src/pubsub.rs b/yazi-dds/src/pubsub.rs
index e2db0362..a9f3795d 100644
--- a/yazi-dds/src/pubsub.rs
+++ b/yazi-dds/src/pubsub.rs
@@ -5,7 +5,7 @@ use mlua::Function;
 use parking_lot::RwLock;
 use yazi_boot::BOOT;
 use yazi_fs::FolderStage;
-use yazi_shared::{Id, RoCell, url::Url};
+use yazi_shared::{Id, RoCell, url::{CovUrl, Url}};
 
 use crate::{Client, ID, PEERS, body::{Body, BodyBulk, BodyHi, BodyMoveItem}};
 
@@ -157,7 +157,7 @@ impl Pubsub {
 
 	pub_after!(rename(tab: Id, from: &Url, to: &Url), (tab, from, to));
 
-	pub_after!(@yank(cut: bool, urls: &HashSet<Url>), (cut, urls));
+	pub_after!(@yank(cut: bool, urls: &HashSet<CovUrl>), (cut, urls));
 
 	pub_after!(move(items: Vec<BodyMoveItem>), (&items), (items));
 
diff --git a/yazi-parser/src/mgr/update_yanked.rs b/yazi-parser/src/mgr/update_yanked.rs
index d1f60874..0d303ce5 100644
--- a/yazi-parser/src/mgr/update_yanked.rs
+++ b/yazi-parser/src/mgr/update_yanked.rs
@@ -4,17 +4,17 @@ use anyhow::bail;
 use mlua::{AnyUserData, ExternalError, IntoLua, Lua, MetaMethod, MultiValue, ObjectLike, UserData, UserDataFields, UserDataMethods, Value};
 use serde::{Deserialize, Serialize};
 use yazi_binding::get_metatable;
-use yazi_shared::{event::CmdCow, url::Url};
+use yazi_shared::{event::CmdCow, url::CovUrl};
 
 type Iter = yazi_binding::Iter<
-	std::iter::Map<std::collections::hash_set::IntoIter<Url>, fn(Url) -> yazi_binding::Url>,
+	std::iter::Map<std::collections::hash_set::IntoIter<CovUrl>, fn(CovUrl) -> yazi_binding::Url>,
 	yazi_binding::Url,
 >;
 
 #[derive(Clone, Debug, Default, Serialize, Deserialize)]
 pub struct UpdateYankedOpt<'a> {
 	pub cut:  bool,
-	pub urls: Cow<'a, HashSet<Url>>,
+	pub urls: Cow<'a, HashSet<CovUrl>>,
 }
 
 impl TryFrom<CmdCow> for UpdateYankedOpt<'_> {
diff --git a/yazi-shared/src/url/component.rs b/yazi-shared/src/url/component.rs
index 164361af..dc5d10f5 100644
--- a/yazi-shared/src/url/component.rs
+++ b/yazi-shared/src/url/component.rs
@@ -74,13 +74,24 @@ impl<'a> Components<'a> {
 	}
 
 	pub fn os_str(&self) -> Cow<'a, OsStr> {
+		let path = self.inner.as_path();
 		if !self.scheme.is_virtual() || self.scheme_yielded {
-			return Cow::Borrowed(self.inner.as_path().as_os_str());
+			return path.as_os_str().into();
 		}
 
-		let mut oss = OsString::from(format!("{}", self.scheme));
-		oss.push(self.inner.as_path());
-		Cow::Owned(oss)
+		let mut s = OsString::from(format!("{}", self.scheme));
+		s.reserve_exact(path.as_os_str().len());
+		s.push(path);
+		s.into()
+	}
+
+	pub fn covariant(&self, other: &Self) -> bool {
+		match (self.scheme_yielded, other.scheme_yielded) {
+			(false, false) => {}
+			(true, true) if self.scheme.covariant(other.scheme) => {}
+			_ => return false,
+		}
+		self.inner == other.inner
 	}
 }
 
diff --git a/yazi-shared/src/url/cov.rs b/yazi-shared/src/url/cov.rs
new file mode 100644
index 00000000..2f33f0a3
--- /dev/null
+++ b/yazi-shared/src/url/cov.rs
@@ -0,0 +1,54 @@
+use std::{hash::{Hash, Hasher}, ops::Deref};
+
+use serde::{Deserialize, Serialize};
+
+use crate::url::Url;
+
+#[derive(Clone, Debug, Deserialize, Eq, Serialize)]
+#[repr(transparent)]
+pub struct CovUrl(pub Url);
+
+impl Deref for CovUrl {
+	type Target = Url;
+
+	fn deref(&self) -> &Self::Target { &self.0 }
+}
+
+impl AsRef<Url> for CovUrl {
+	fn as_ref(&self) -> &Url { &self.0 }
+}
+
+impl From<Url> for CovUrl {
+	fn from(value: Url) -> Self { Self(value) }
+}
+
+impl From<CovUrl> for Url {
+	fn from(value: CovUrl) -> Self { value.0 }
+}
+
+impl Hash for CovUrl {
+	fn hash<H: Hasher>(&self, state: &mut H) {
+		self.loc.hash(state);
+		if self.scheme.is_virtual() {
+			self.scheme.hash(state);
+		}
+	}
+}
+
+impl PartialEq for CovUrl {
+	fn eq(&self, other: &Self) -> bool { self.covariant(other) }
+}
+
+impl PartialEq<Url> for CovUrl {
+	fn eq(&self, other: &Url) -> bool { self.covariant(other) }
+}
+
+impl CovUrl {
+	#[inline]
+	pub fn new<T: AsRef<Url>>(u: &T) -> &Self {
+		unsafe { &*(u.as_ref() as *const Url as *const Self) }
+	}
+
+	#[inline]
+	pub fn parent_url(&self) -> Option<CovUrl> { self.0.parent_url().map(CovUrl) }
+}
diff --git a/yazi-shared/src/url/loc.rs b/yazi-shared/src/url/loc.rs
index 17db445b..7c48d651 100644
--- a/yazi-shared/src/url/loc.rs
+++ b/yazi-shared/src/url/loc.rs
@@ -15,6 +15,10 @@ impl Deref for Loc {
 	fn deref(&self) -> &Self::Target { &self.inner }
 }
 
+impl AsRef<Path> for Loc {
+	fn as_ref(&self) -> &Path { &self.inner }
+}
+
 impl PartialEq for Loc {
 	fn eq(&self, other: &Self) -> bool { self.inner == other.inner }
 }
diff --git a/yazi-shared/src/url/mod.rs b/yazi-shared/src/url/mod.rs
index b9aa25b3..08f48576 100644
--- a/yazi-shared/src/url/mod.rs
+++ b/yazi-shared/src/url/mod.rs
@@ -1 +1 @@
-yazi_macro::mod_flat!(component display loc scheme url urn);
+yazi_macro::mod_flat!(component cov display loc scheme url urn);
diff --git a/yazi-shared/src/url/scheme.rs b/yazi-shared/src/url/scheme.rs
index 3034fa4c..948f05a7 100644
--- a/yazi-shared/src/url/scheme.rs
+++ b/yazi-shared/src/url/scheme.rs
@@ -47,17 +47,9 @@ impl Scheme {
 		})
 	}
 
+	#[inline]
 	pub fn covariant(&self, other: &Self) -> bool {
-		match (self, other) {
-			// Local files
-			(
-				Self::Regular | Self::Search(_) | Self::SearchItem,
-				Self::Regular | Self::Search(_) | Self::SearchItem,
-			) => true,
-
-			// Virtual files within the same namespace
-			(a, b) => a == b,
-		}
+		if self.is_virtual() || other.is_virtual() { self == other } else { true }
 	}
 
 	#[inline]
diff --git a/yazi-shared/src/url/url.rs b/yazi-shared/src/url/url.rs
index 7217d9ac..1540624f 100644
--- a/yazi-shared/src/url/url.rs
+++ b/yazi-shared/src/url/url.rs
@@ -1,4 +1,4 @@
-use std::{borrow::Cow, ffi::OsStr, fmt::{Debug, Formatter}, hash::{BuildHasher, Hash, Hasher}, ops::Deref, path::{Path, PathBuf}};
+use std::{borrow::Cow, ffi::OsStr, fmt::{Debug, Formatter}, hash::BuildHasher, ops::Deref, path::{Path, PathBuf}};
 
 use percent_encoding::percent_decode;
 use serde::{Deserialize, Serialize};
@@ -6,7 +6,7 @@ use serde::{Deserialize, Serialize};
 use super::UrnBuf;
 use crate::{IntoOsStr, url::{Components, Display, Loc, Scheme}};
 
-#[derive(Clone, Default, Eq, Ord, PartialOrd)]
+#[derive(Clone, Default, Eq, Ord, PartialOrd, PartialEq, Hash)]
 pub struct Url {
 	pub loc:    Loc,
 	pub scheme: Scheme,
@@ -18,19 +18,6 @@ impl Deref for Url {
 	fn deref(&self) -> &Self::Target { &self.loc }
 }
 
-impl Debug for Url {
-	fn fmt(&self, f: &mut Formatter<'_>) -> std::fmt::Result {
-		let Self { scheme, loc } = self;
-		match scheme {
-			Scheme::Regular => write!(f, "{scheme}{}", loc.display()),
-			Scheme::Search(_) => write!(f, "{scheme}{}", loc.display()),
-			Scheme::SearchItem => write!(f, "{scheme}{}", loc.display()),
-			Scheme::Archive(_) => write!(f, "{scheme}{}", loc.display()),
-			Scheme::Sftp(_) => write!(f, "{scheme}{}", loc.display()),
-		}
-	}
-}
-
 impl From<Loc> for Url {
 	fn from(loc: Loc) -> Self { Self { loc, scheme: Scheme::Regular } }
 }
@@ -165,7 +152,7 @@ impl Url {
 		}
 
 		Some(Self {
-			loc:    self.loc.strip_prefix(base.loc.as_path()).ok()?.into(),
+			loc:    self.loc.strip_prefix(&base.loc).ok()?.into(),
 			scheme: self.scheme.clone(),
 		})
 	}
@@ -229,36 +216,9 @@ impl Url {
 	pub fn into_path(self) -> PathBuf { self.loc.into_path() }
 }
 
-impl Hash for Url {
-	fn hash<H: Hasher>(&self, state: &mut H) {
-		self.loc.hash(state);
-
-		match &self.scheme {
-			Scheme::Regular => {}
-			Scheme::Search(_) => {
-				self.scheme.hash(state);
-			}
-			Scheme::SearchItem => {}
-			Scheme::Archive(_) => {
-				self.scheme.hash(state);
-			}
-			Scheme::Sftp(_) => {
-				self.scheme.hash(state);
-			}
-		}
-	}
-}
-
-impl PartialEq for Url {
-	fn eq(&self, other: &Self) -> bool {
-		if self.loc != other.loc {
-			return false;
-		}
-
-		match (&self.scheme, &other.scheme) {
-			(Scheme::Regular | Scheme::SearchItem, Scheme::Regular | Scheme::SearchItem) => true,
-			_ => self.scheme == other.scheme,
-		}
+impl Debug for Url {
+	fn fmt(&self, f: &mut Formatter<'_>) -> std::fmt::Result {
+		write!(f, "{}{}", self.scheme, self.loc.display())
 	}
 }