Theorems · Theorem · category theory
CategoryTheory.Iso.hom_inv_id
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} (self : X ≅ Y),
CategoryTheory.CategoryStruct.comp self.hom self.inv = CategoryTheory.CategoryStruct.id XComposition of the two directions of an isomorphism is the identity on the source.
- Defined in
- Mathlib.CategoryTheory.Iso
- Cited by
- 264 results in Mathlib
- Foundations
- Depth 3 from the axioms, rests on 12 definitions · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.Iso.homstatement · cited by 7,684
- CategoryTheory.Iso.invstatement · cited by 6,514
- CategoryTheory.CategoryStruct.idstatement · cited by 6,235
- CategoryTheory.Isostatement and proof · cited by 3,963
Cited by266
Results whose statement or proof uses this declaration.
- CategoryTheory.Iso.hom_inv_id_assocproof · cited by 187
- CategoryTheory.Iso.hom_inv_id_applyproof · cited by 50
- CategoryTheory.Iso.comp_inv_eqproof · cited by 41
- CategoryTheory.MonoidalCategory.whiskerRight_idproof · cited by 38
- CategoryTheory.MonoidalCategory.tensor_whiskerLeftproof · cited by 37
- CategoryTheory.MonoidalCategory.whisker_assocproof · cited by 31
- CategoryTheory.MonoidalCategory.id_whiskerLeftproof · cited by 29
- CategoryTheory.IsPullback.of_isoproof · cited by 17
- CategoryTheory.BraidedCategory.braiding_tensor_left_homproof · cited by 13
- CategoryTheory.MonoidalCategory.associator_inv_naturality_leftproof · cited by 9
- CategoryTheory.braiding_tensorUnit_leftproof · cited by 7
- CategoryTheory.Bicategory.hom_inv_whiskerRightproof · cited by 6
Showing the 200 most cited of 266.