Theorems · Theorem · category theory

CategoryTheory.SmallObject.functor_map

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {I : Type w} {A B : I → C} (f : (i : I) → A i ⟶ B i)
  [inst_1 : CategoryTheory.Limits.HasPushouts C]
  [inst_2 :
    ∀ {X S : C} (πX : X ⟶ S),
      CategoryTheory.Limits.HasColimitsOfShape
        (CategoryTheory.Discrete (CategoryTheory.SmallObject.FunctorObjIndex f πX)) C]
  {π₁ π₂ : CategoryTheory.Arrow C} (τ : π₁ ⟶ π₂),
  (CategoryTheory.SmallObject.functor f).map τ =
    CategoryTheory.Arrow.homMk (CategoryTheory.SmallObject.functorMap f τ) (CategoryTheory.Arrow.Hom.right τ) ⋯

Defined in

Mathlib.CategoryTheory.SmallObject.Construction

Cited by

0 results in Mathlib

Foundations

Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPushoutsCategoryTheory.Limits.HasColimitsOfShape