Theorems · Theorem · category theory

CategoryTheory.Square.IsPushout.map_iff

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {D : Type u'} [inst_1 : CategoryTheory.Category.{v', u'} D]
  (sq : CategoryTheory.Square C) (F : CategoryTheory.Functor C D)
  [CategoryTheory.Limits.PreservesColimit (CategoryTheory.Limits.span sq.f₁₂ sq.f₁₃) F]
  [CategoryTheory.Limits.ReflectsColimit (CategoryTheory.Limits.span sq.f₁₂ sq.f₁₃) F],
  (sq.map F).IsPushout ↔ sq.IsPushout

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Shapes.Square

Cited by

0 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.PreservesColimitCategoryTheory.Limits.ReflectsColimit