Theorems · Theorem · category theory

CategoryTheory.NatTrans.epi_iff_epi_app

∀ {K : Type u} [inst : CategoryTheory.Category.{v, u} K] {C : Type u'} [inst_1 : CategoryTheory.Category.{v', u'} C]
  {F G : CategoryTheory.Functor K C} (f : F ⟶ G) [CategoryTheory.Limits.HasPushouts C],
  CategoryTheory.Epi f ↔ ∀ (k : K), CategoryTheory.Epi (f.app k)

Defined in

Mathlib.CategoryTheory.Limits.FunctorCategory.EpiMono

Cited by

4 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasPushouts