Theorems · Theorem · category theory

CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceFunctor_map_left

∀ {T : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} T] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {C : Type u₃} [inst_2 : CategoryTheory.Category.{v₃, u₃} C] (F : CategoryTheory.Functor C T)
  (G : CategoryTheory.Functor D T) (c : C) {X Y : CategoryTheory.CostructuredArrow (CategoryTheory.Comma.fst F G) c}
  (f : X ⟶ Y),
  ((CategoryTheory.CostructuredArrow.ofCommaFstEquivalenceFunctor F G c).map f).left =
    CategoryTheory.Over.homMk f.left.left ⋯

Defined in

Mathlib.CategoryTheory.Comma.Over.Basic

Cited by

0 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category