diff --git a/namedisl/set_like.py b/namedisl/set_like.py
index 0fee3a3..07e25b3 100644
--- a/namedisl/set_like.py
+++ b/namedisl/set_like.py
@@ -189,6 +189,7 @@ class _NamedIslSetOrMapLike(NamedIslObject[IslSetOrMapLikeT_co]):
     .. automethod:: project_out
     .. automethod:: project_out_except
     .. automethod:: gist
+    .. automethod:: detect_equalities
     .. automethod:: remove_divs
     .. automethod:: compute_divs
     .. automethod:: __and__
@@ -312,6 +313,12 @@ def gist(self, context: Self) -> Self:
             self_aligned.space,
         )
 
+    def detect_equalities(self) -> Self:
+        return type(self)(
+            cast("IslSetOrMapLikeT_co", self._obj.detect_equalities()),
+            self.space,
+        )
+
     def compute_divs(self) -> Self:
         return type(self)(
             cast("IslSetOrMapLikeT_co", self._obj.compute_divs()),
@@ -738,6 +745,9 @@ def make_map_from_domain_and_range(
 class Map(_NamedIslMapLike[isl.Map], _NamedIslUnbasic[isl.Map]):
     """
     .. automethod:: is_bijective
+    .. automethod:: is_injective
+    .. automethod:: is_single_valued
+    .. automethod:: lexmin
     .. automethod:: complement
     .. automethod:: simple_hull
     .. automethod:: convex_hull
@@ -756,9 +766,18 @@ class Map(_NamedIslMapLike[isl.Map], _NamedIslUnbasic[isl.Map]):
 
     _isl_type: ClassVar[type[IslObject]] = isl.Map
 
-    def is_bijective(self):
+    def is_bijective(self) -> bool:
         return self._obj.is_bijective()
 
+    def is_injective(self) -> bool:
+        return self._obj.is_injective()
+
+    def is_single_valued(self) -> bool:
+        return self._obj.is_single_valued()
+
+    def lexmin(self) -> Map:
+        return Map(self._obj.lexmin(), self.space)
+
     def complement(self) -> Map:
         return Map(self._obj.complement(), self.space)
 
diff --git a/namedisl/test/test_set_like.py b/namedisl/test/test_set_like.py
index a4cabea..83b4df7 100644
--- a/namedisl/test/test_set_like.py
+++ b/namedisl/test/test_set_like.py
@@ -315,6 +315,41 @@ def test_map_coalesce() -> None:
     assert len(map_.coalesce().basic_maps()) == 1
 
 
+def test_map_detect_equalities() -> None:
+    map_ = nisl.make_map("{ [i] -> [j] : 0 <= i <= j < 5 }")
+    detected = map_.detect_equalities()
+
+    assert isinstance(detected, nisl.Map)
+    assert detected.space == map_.space
+    assert detected.equals(map_)
+
+
+def test_map_function_properties() -> None:
+    bijective = nisl.make_map("{ [i] -> [j = i] : 0 <= i < 2 }")
+    many_to_one = nisl.make_map("{ [i] -> [j = 0] : 0 <= i < 2 }")
+    one_to_many = nisl.make_map("{ [i = 0] -> [j] : 0 <= j < 2 }")
+
+    assert bijective.is_bijective()
+    assert bijective.is_injective()
+    assert bijective.is_single_valued()
+
+    assert not many_to_one.is_bijective()
+    assert not many_to_one.is_injective()
+    assert many_to_one.is_single_valued()
+
+    assert not one_to_many.is_bijective()
+    assert one_to_many.is_injective()
+    assert not one_to_many.is_single_valued()
+
+
+def test_map_lexmin_preserves_named_space() -> None:
+    map_ = nisl.make_map(
+        "{ [target] -> [source] : target = 0 and 1 <= source <= 2 }"
+    )
+
+    assert map_.lexmin() == nisl.make_map("{ [target = 0] -> [source = 1] }")
+
+
 @pytest.mark.parametrize("ndims_domain", [2, 3, 4, 5])
 @pytest.mark.parametrize("ndims_range", [2, 3, 4, 5])
 @pytest.mark.parametrize("has_params", [True, False])