Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.Arrow.PushoutProduct.hasLiftingProperty_mk_isInitial_isTerminal_iff

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasPushouts C]
  [inst_2 : CategoryTheory.CartesianMonoidalCategory C] [inst_3 : CategoryTheory.MonoidalClosed C]
  [CategoryTheory.BraidedCategory C] {A B K L X Y : C} {g : K ⟶ L} (i : CategoryTheory.Limits.IsInitial A)
  (t : CategoryTheory.Limits.IsTerminal Y),
  CategoryTheory.HasLiftingProperty (CategoryTheory.Arrow.mk (i.to B) □ CategoryTheory.Arrow.mk g).hom (t.from X) ↔
    CategoryTheory.HasLiftingProperty g (t.from (B ⟹ X))

(∅ ⟶ B) □ g lifts against X ⟶ ⋆ if and only if g lifts against (B ⟹ X) ⟶ ⋆.

Defined in

Mathlib.CategoryTheory.LiftingProperties.PushoutProduct

Cited by

0 results in Mathlib

Foundations

Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPushoutsCategoryTheory.CartesianMonoidalCategoryCategoryTheory.MonoidalClosedCategoryTheory.BraidedCategory