Theorems · Theorem · category theory

CategoryTheory.regularTopology.equalizerCondition_precomp_of_preservesPullback

∀ {C : Type u_1} {D : Type u_2} {E : Type u_3} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] [inst_2 : CategoryTheory.Category.{v_3, u_3} E]
  (P : CategoryTheory.Functor Cᵒᵖ D) (F : CategoryTheory.Functor E C)
  [∀ {X B : E} (π : X ⟶ B) [CategoryTheory.EffectiveEpi π],
      CategoryTheory.Limits.PreservesLimit (CategoryTheory.Limits.cospan π π) F]
  [F.PreservesEffectiveEpis],
  CategoryTheory.regularTopology.EqualizerCondition P → CategoryTheory.regularTopology.EqualizerCondition (F.op.comp P)

Precomposing with a pullback-preserving functor preserves the equalizer condition.

Defined in

Mathlib.CategoryTheory.Sites.Coherent.RegularSheaves

Cited by

1 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.PreservesLimitCategoryTheory.Functor.PreservesEffectiveEpis