Theorems · Theorem · category theory
CategoryTheory.Endofunctor.Adjunction.Coalgebra.homEquiv_naturality_str_symm
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {F G : CategoryTheory.Functor C C} (adj : F ⊣ G)
(V₁ V₂ : CategoryTheory.Endofunctor.Coalgebra G) (f : V₁ ⟶ V₂),
CategoryTheory.CategoryStruct.comp (F.map f.f) ((adj.homEquiv V₂.V V₂.V).symm V₂.str) =
CategoryTheory.CategoryStruct.comp ((adj.homEquiv V₁.V V₁.V).symm V₁.str) f.f- Cited by
- 0 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- 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 and proof · cited by 17,999
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapstatement · cited by 8,698
- Equivstatement · cited by 8,337
- Equiv.symmstatement and proof · cited by 3,681
- CategoryTheory.Adjunctionstatement and proof · cited by 524
- CategoryTheory.Adjunction.homEquivstatement and proof · cited by 202
- CategoryTheory.Endofunctor.Coalgebrastatement and proof · cited by 70
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.Endofunctor.Adjunction.Coalgebra.toAlgebraOfproof · cited by 11