Theorems · Theorem · category theory
CategoryTheory.Localization.SmallHom.mk_id_comp
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {W : CategoryTheory.MorphismProperty C} {X Y : C}
[inst_1 : CategoryTheory.Localization.HasSmallLocalizedHom W X Y]
[inst_2 : CategoryTheory.Localization.HasSmallLocalizedHom W X X] (α : CategoryTheory.Localization.SmallHom W X Y),
(CategoryTheory.Localization.SmallHom.mk W (CategoryTheory.CategoryStruct.id X)).comp α = α- Cited by
- 1 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.CategoryStruct.idstatement and proof · cited by 6,235
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.Category.id_compproof · cited by 1,998
- CategoryTheory.Functor.map_idproof · cited by 616
- Equiv.injectiveproof · cited by 464
- CategoryTheory.MorphismProperty.Qproof · cited by 98
- CategoryTheory.Localization.HasSmallLocalizedHomstatement and proof · cited by 30
- CategoryTheory.Localization.SmallHom.equivproof · cited by 25
- CategoryTheory.Localization.SmallHomstatement and proof · cited by 24
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.LocalizerMorphism.smallHomMap'_compproof · cited by 0