Theorems · Theorem · category theory

CategoryTheory.SimplicialObject.Augmented.w_app

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : CategoryTheory.SimplicialObject.Augmented C} (f : X ⟶ Y)
  (n : SimplexCategoryᵒᵖ),
  CategoryTheory.CategoryStruct.comp (f.left.app n) (Y.hom.app n) =
    CategoryTheory.CategoryStruct.comp (X.hom.app n) f.right

Defined in: Mathlib.AlgebraicTopology.SimplicialObject.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

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Cites18

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 · cited by 19,642
CategoryTheory.CategoryStruct.compstatement · cited by 17,999
Oppositestatement and proof · cited by 8,081
CategoryTheory.NatTrans.appstatement · cited by 7,406
CategoryTheory.Functor.idstatement · cited by 3,333
SimplexCategorystatement and proof · cited by 2,204
CategoryTheory.Comma.leftstatement · cited by 886
CategoryTheory.Comma.rightstatement · cited by 727
CategoryTheory.SimplicialObjectstatement · cited by 548
CategoryTheory.CommaMorphism.leftstatement · cited by 526

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.SimplicialObject.Augmented.w_app_assocproof · cited by 0