Theorems · Inductive type · category theory

CategoryTheory.Limits.CatCospanTransform

{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] →
            CategoryTheory.Functor A B →
              CategoryTheory.Functor C B →
                {A' : Type u₄} →
                  {B' : Type u₅} →
                    {C' : Type u₆} →
                      [inst : CategoryTheory.Category.{v₄, u₄} A'] →
                        [inst_3 : CategoryTheory.Category.{v₅, u₅} B'] →
                          [inst_4 : CategoryTheory.Category.{v₆, u₆} C'] →
                            CategoryTheory.Functor A' B' →
                              CategoryTheory.Functor C' B' →
                                Type
                                  (max
                                      (max
                                          (max
                                              (max (max (max (max (max (max (max (max u₁ u₂) u₃) u₄) u₅) u₆) v₁) v₂) v₃)
                                              v₄)
                                          v₅)
                                      v₆)

A CatCospanTransform F G F' G' is a diagram `` F G A ⥤ B ⥢ C H₁| |H₂ |H₃ v v v A'⥤ B'⥢ C' F' G' ` with specified CatCommSq`s expressing 2-commutativity of the squares.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform

Cited by

132 results in Mathlib

Foundations

Depth 2 from the axioms, rests on 3 definitions · uses no axioms

Assumes

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