Theorems · Theorem · category theory

CategoryTheory.TransfiniteCompositionOfShape.fac_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {J : Type w} [inst_1 : LinearOrder J] [inst_2 : OrderBot J]
  {X Y : C} {f : X ⟶ Y} [inst_3 : SuccOrder J] [inst_4 : WellFoundedLT J]
  (self : CategoryTheory.TransfiniteCompositionOfShape J f) {Z : C}
  (h : ((CategoryTheory.Functor.const J).obj Y).obj ⊥ ⟶ Z),
  CategoryTheory.CategoryStruct.comp self.isoBot.inv (CategoryTheory.CategoryStruct.comp (self.incl.app ⊥) h) =
    CategoryTheory.CategoryStruct.comp f h

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Preorder.TransfiniteCompositionOfShape

Cited by

1 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryLinearOrderOrderBotSuccOrderWellFoundedLT