Theorems · Theorem · category theory

CategoryTheory.IsCofiltered.eq_condition_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.IsCofilteredOrEmpty C] {j j' : C}
  (f f' : j ⟶ j') {Z : C} (h : j' ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.IsCofiltered.eqHom f f') (CategoryTheory.CategoryStruct.comp f h) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.IsCofiltered.eqHom f f')
      (CategoryTheory.CategoryStruct.comp f' h)

eq_condition f f', for morphisms f f' : j ⟶ j', is the proof that eqHom f f' ≫ f = eqHom f f' ≫ f'.

Defined in

Mathlib.CategoryTheory.Filtered.Basic

Cited by

0 results in Mathlib

Foundations

Depth 13 from the axioms · uses Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.IsCofilteredOrEmpty