Theorems · Theorem · category theory

CategoryTheory.regularTopology.mapToEqualizer_eq_comp

∀ {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) [inst_1 : CategoryTheory.Limits.HasPullback π π],
  CategoryTheory.regularTopology.mapToEqualizer P π (CategoryTheory.Limits.pullback.fst π π)
      (CategoryTheory.Limits.pullback.snd π π) ⋯ =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.equalizer.lift (P.map π.op) ⋯)
      (CategoryTheory.Limits.Types.equalizerIso (P.map (CategoryTheory.Limits.pullback.fst π π).op)
          (P.map (CategoryTheory.Limits.pullback.snd π π).op)).hom

Defined in

Mathlib.CategoryTheory.Sites.Coherent.RegularSheaves

Cited by

1 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullback