Theorems · Theorem · category theory

CategoryTheory.regularTopology.EqualizerCondition.mk

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] (P : CategoryTheory.Functor Cᵒᵖ (Type u_4)),
  (∀ (X B : C) (π : X ⟶ B) [CategoryTheory.EffectiveEpi π] [inst_2 : CategoryTheory.Limits.HasPullback π π],
      Function.Bijective
        ⇑(CategoryTheory.ConcreteCategory.hom
            (CategoryTheory.regularTopology.mapToEqualizer P π (CategoryTheory.Limits.pullback.fst π π)
              (CategoryTheory.Limits.pullback.snd π π) ⋯))) →
    CategoryTheory.regularTopology.EqualizerCondition P

Defined in

Mathlib.CategoryTheory.Sites.Coherent.RegularSheaves

Cited by

2 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category