Theorems · Definition · category theory

CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform

{A : Type u₁} →
  {B : Type u₂} →
    {C : Type u₃} →
      [inst : CategoryTheory.Category.{v₁, u₁} A] →
        [inst_1 : CategoryTheory.Category.{v₂, u₂} B] →
          [inst_2 : CategoryTheory.Category.{v₃, u₃} C] →
            {F : CategoryTheory.Functor A B} →
              {G : CategoryTheory.Functor C B} →
                {A₁ : Type u₄} →
                  {B₁ : Type u₅} →
                    {C₁ : Type u₆} →
                      [inst_3 : CategoryTheory.Category.{v₄, u₄} A₁] →
                        [inst_4 : CategoryTheory.Category.{v₅, u₅} B₁] →
                          [inst_5 : CategoryTheory.Category.{v₆, u₆} C₁] →
                            {F₁ : CategoryTheory.Functor A₁ B₁} →
                              {G₁ : CategoryTheory.Functor C₁ B₁} →
                                (X : Type u₇) →
                                  [inst_6 : CategoryTheory.Category.{v₇, u₇} X] →
                                    CategoryTheory.Functor (CategoryTheory.Limits.CatCospanTransform F G F₁ G₁)
                                      (CategoryTheory.Functor
                                        (CategoryTheory.Limits.CategoricalPullback.CatCommSqOver F G X)
                                        (CategoryTheory.Limits.CategoricalPullback.CatCommSqOver F₁ G₁ X))

Functorially transform a CatCommSqOver F G X by whiskering it with a CatCospanTransform.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.Basic

Cited by

37 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category