Theorems · Theorem · category theory
CategoryTheory.Equivalence.inverse_counitInv_comp_assoc
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
(e : C ≌ D) (Y : D) {Z : C} (h : e.inverse.obj Y ⟶ Z),
CategoryTheory.CategoryStruct.comp (e.inverse.map (e.counitInv.app Y))
(CategoryTheory.CategoryStruct.comp (e.unitInv.app (e.inverse.obj Y)) h) =
h- Defined in
- Mathlib.CategoryTheory.Equivalence
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 26 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.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.Functor.mapstatement and proof · cited by 8,698
- CategoryTheory.NatTrans.appstatement and proof · cited by 7,406
- CategoryTheory.Functor.compstatement · cited by 6,529
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.Functor.idstatement · cited by 3,333
- CategoryTheory.Category.id_compproof · cited by 1,998
- CategoryTheory.Equivalence.functorstatement · cited by 1,268
- CategoryTheory.Equivalence.inversestatement and proof · cited by 1,130
Cited by2
Results whose statement or proof uses this declaration.