Theorems · Inductive type · category theory

CategoryTheory.Limits.CategoricalPullback.CatCommSqOver

{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 →
                (X : Type u₄) →
                  [CategoryTheory.Category.{v₄, u₄} X] → Type (max (max (max (max (max (max u₁ u₃) u₄) v₁) v₂) v₃) v₄)

The data of a categorical commutative square over a cospan F, G with cone point X is that of a functor T : X ⥤ A, a functor L : X ⥤ C, and a CatCommSq T L F G. Note that this is exactly what an object of ((whiskeringRight X A B).obj F) ⊡ ((whiskeringRight X C B).obj G) is, so CatCommSqOver F G X is in equivalent to ((whiskeringRight X A B).obj F) ⊡ ((whiskeringRight X C B).obj G), though it is defined separately for performance reasons.

Defined in

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

Cited by

135 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category