Theorems · Theorem · category theory

CategoryTheory.Limits.end_.condition

∀ {J : Type u} [inst : CategoryTheory.Category.{v, u} J] {C : Type u'} [inst_1 : CategoryTheory.Category.{v', u'} C]
  (F : CategoryTheory.Functor Jᵒᵖ (CategoryTheory.Functor J C)) [inst_2 : CategoryTheory.Limits.HasEnd F] {i j : J}
  (f : i ⟶ j),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.end_.π F i) ((F.obj (Opposite.op i)).map f) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.end_.π F j) ((F.map f.op).app j)

Defined in

Mathlib.CategoryTheory.Limits.Shapes.End

Cited by

3 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasEnd