Theorems · Definition · category theory

CategoryTheory.Limits.CatCospanTransform.comp

{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} →
                {A' : Type u₄} →
                  {B' : Type u₅} →
                    {C' : Type u₆} →
                      [inst_3 : CategoryTheory.Category.{v₄, u₄} A'] →
                        [inst_4 : CategoryTheory.Category.{v₅, u₅} B'] →
                          [inst_5 : CategoryTheory.Category.{v₆, u₆} C'] →
                            {F' : CategoryTheory.Functor A' B'} →
                              {G' : CategoryTheory.Functor C' B'} →
                                {A'' : Type u₇} →
                                  {B'' : Type u₈} →
                                    {C'' : Type u₉} →
                                      [inst_6 : CategoryTheory.Category.{v₇, u₇} A''] →
                                        [inst_7 : CategoryTheory.Category.{v₈, u₈} B''] →
                                          [inst_8 : CategoryTheory.Category.{v₉, u₉} C''] →
                                            {F'' : CategoryTheory.Functor A'' B''} →
                                              {G'' : CategoryTheory.Functor C'' B''} →
                                                CategoryTheory.Limits.CatCospanTransform F G F' G' →
                                                  CategoryTheory.Limits.CatCospanTransform F' G' F'' G'' →
                                                    CategoryTheory.Limits.CatCospanTransform F G F'' G''

Composition of CatCospanTransforms is defined "componentwise".

Defined in

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

Cited by

63 results in Mathlib

Foundations

Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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