Theorems · Theorem · category theory

CategoryTheory.regularTopology.equalizerCondition_iff_isIso_lift

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] (P : CategoryTheory.Functor Cᵒᵖ (Type u_4)),
  CategoryTheory.regularTopology.EqualizerCondition P ↔
    ∀ (X B : C) (π : X ⟶ B) [CategoryTheory.EffectiveEpi π] [inst_2 : CategoryTheory.Limits.HasPullback π π],
      CategoryTheory.IsIso (CategoryTheory.Limits.equalizer.lift (P.map π.op) ⋯)

An alternative phrasing of the explicit equalizer condition, using more categorical language.

Defined in

Mathlib.CategoryTheory.Sites.Coherent.RegularSheaves

Cited by

0 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category