Theorems · Theorem · category theory
CategoryTheory.cosimplicialSimplicialEquiv_functor_obj_obj
∀ (C : Type u) [inst : CategoryTheory.Category.{v, u} C] (F : (CategoryTheory.Functor SimplexCategory C)ᵒᵖ)
(X : SimplexCategoryᵒᵖ),
((CategoryTheory.cosimplicialSimplicialEquiv C).functor.obj F).obj X =
Opposite.op ((Opposite.unop F).obj (Opposite.unop X))- Cited by
- 0 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
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Cites10
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
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- Oppositestatement and proof · cited by 8,081
- Opposite.unopstatement · cited by 2,231
- SimplexCategorystatement and proof · cited by 2,204
- CategoryTheory.Equivalence.functorstatement and proof · cited by 1,268
- CategoryTheory.SimplicialObjectstatement · cited by 548
- CategoryTheory.CosimplicialObjectstatement · cited by 125
- CategoryTheory.cosimplicialSimplicialEquivstatement and proof · cited by 11
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