Theorems · Theorem · category theory

CategoryTheory.Idempotents.functorExtension_map_app

∀ (C : Type u_1) (D : Type u_2) [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] [inst_2 : CategoryTheory.IsIdempotentComplete D]
  {X Y : CategoryTheory.Functor C D} (f : X ⟶ Y) (X_1 : CategoryTheory.Idempotents.Karoubi C),
  ((CategoryTheory.Idempotents.functorExtension C D).map f).app X_1 =
    (CategoryTheory.Idempotents.toKaroubiEquivalence D).inverse.map
      (((CategoryTheory.Idempotents.functorExtension₂ C D).map f).app X_1)

Defined in

Mathlib.CategoryTheory.Idempotents.FunctorExtension

Cited by

0 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.IsIdempotentComplete