Theorems · Theorem · category theory

CategoryTheory.Idempotents.whiskeringLeft_obj_preimage_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]
  {F G : CategoryTheory.Functor (CategoryTheory.Idempotents.Karoubi C) D}
  (τ : (CategoryTheory.Idempotents.toKaroubi C).comp F ⟶ (CategoryTheory.Idempotents.toKaroubi C).comp G)
  (P : CategoryTheory.Idempotents.Karoubi C),
  (((CategoryTheory.Functor.whiskeringLeft C (CategoryTheory.Idempotents.Karoubi C) D).obj
              (CategoryTheory.Idempotents.toKaroubi C)).preimage
          τ).app
      P =
    CategoryTheory.CategoryStruct.comp (F.map P.decompId_i)
      (CategoryTheory.CategoryStruct.comp (τ.app P.X) (G.map P.decompId_p))

Defined in

Mathlib.CategoryTheory.Idempotents.FunctorExtension

Cited by

2 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.IsIdempotentComplete