Theorems · Definition · category theory

CategoryTheory.Sum.natTransOfWhiskerLeftInlInr

{A : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} A] →
    {A' : Type u_2} →
      [inst_1 : CategoryTheory.Category.{v_2, u_2} A'] →
        {B : Type u} →
          [inst_2 : CategoryTheory.Category.{v, u} B] →
            {F G : CategoryTheory.Functor (A ⊕ A') B} →
              ((CategoryTheory.Sum.inl_ A A').comp F ⟶ (CategoryTheory.Sum.inl_ A A').comp G) →
                ((CategoryTheory.Sum.inr_ A A').comp F ⟶ (CategoryTheory.Sum.inr_ A A').comp G) → (F ⟶ G)

A consequence of functorEquiv: we can construct a natural transformation of functors A ⊕ A' ⥤ B from the data of natural transformations of their whiskering with inl_ and inr_.

Defined in

Mathlib.CategoryTheory.Sums.Products

Cited by

5 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category