Theorems · Theorem · category theory

CategoryTheory.TwoSquare.costructuredArrowRightwards_map

∀ {C₁ : Type u₁} {C₂ : Type u₂} {C₃ : Type u₃} {C₄ : Type u₄} [inst : CategoryTheory.Category.{v₁, u₁} C₁]
  [inst_1 : CategoryTheory.Category.{v₂, u₂} C₂] [inst_2 : CategoryTheory.Category.{v₃, u₃} C₃]
  [inst_3 : CategoryTheory.Category.{v₄, u₄} C₄] {T : CategoryTheory.Functor C₁ C₂} {L : CategoryTheory.Functor C₁ C₃}
  {R : CategoryTheory.Functor C₂ C₄} {B : CategoryTheory.Functor C₃ C₄} (w : CategoryTheory.TwoSquare T L R B) (X₃ : C₃)
  {X Y : CategoryTheory.CostructuredArrow L X₃} (f : X ⟶ Y),
  (w.costructuredArrowRightwards X₃).map f =
    (CategoryTheory.CostructuredArrow.pre T R (B.obj X₃)).map
      ((CategoryTheory.Comma.mapLeft (CategoryTheory.Functor.fromPUnit (B.obj X₃)) w).map
        (CategoryTheory.CostructuredArrow.homMk f.left ⋯))

Defined in

Mathlib.CategoryTheory.GuitartExact.Basic

Cited by

0 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category