fact: Definition isSheaf (P : Presheaf) (GT : GrothendieckTopology) : UU := ∏ (c : C) (S : sieve c) (isCOS : GrothendieckTopology_COS GT c S) (τ : nat_trans (sieve_functor S) (PresheafToFunctor P)), iscontr (∑ η : nat_trans (FunctorPrecatObToFunctor (yoneda C c)) (PresheafToFunctor P), nat_trans_comp _ _ _ (sieve_nat_trans S) η = τ).
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.Limits.Products UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.slicecat UniMath.CategoryTheory.Monics UniMath.CategoryTheory.Subobjects UniMath.CategoryTheory.yoneda UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.Limits UniMath.CategoryTheory.Limits.Graphs.Pullbacks UniMath.CategoryTheory.Limits.Graphs.Equalizers UniMath.CategoryTheory.Subcategory.Core UniMath.CategoryTheory.Subcategory.Full UniMath.CategoryTheory.Equivalences.Core