Theorems · Definition · category theory

CategoryTheory.TwoSquare

{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] →
                CategoryTheory.Functor C₁ C₂ →
                  CategoryTheory.Functor C₁ C₃ →
                    CategoryTheory.Functor C₂ C₄ → CategoryTheory.Functor C₃ C₄ → Type (max u₁ v₄)

A 2-square consists of a natural transformation T ⋙ R ⟶ L ⋙ B involving fours functors T, L, R, B that are on the top/left/right/bottom sides of a square of categories.

Defined in

Mathlib.CategoryTheory.Functor.TwoSquare

Cited by

100 results in Mathlib

Foundations

Depth 20 from the axioms, rests on 106 definitions · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category