Theorems · Theorem · category theory

TopCat.Presheaf.isSheaf_iff_isSheafEqualizerProducts

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasProducts C] {X : TopCat}
  (F : TopCat.Presheaf C X), F.IsSheaf ↔ F.IsSheafEqualizerProducts

The sheaf condition in terms of an equalizer diagram is equivalent to the default sheaf condition.

Defined in

Mathlib.Topology.Sheaves.SheafCondition.EqualizerProducts

Cited by

0 results in Mathlib

Foundations

Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasProducts