Theorems · Theorem · category theory

CategoryTheory.Sheaf.Hom.mono_of_presheaf_mono

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] (J : CategoryTheory.GrothendieckTopology C) (A : Type u₂)
  [inst_1 : CategoryTheory.Category.{v₂, u₂} A] {F G : CategoryTheory.Sheaf J A} (f : F ⟶ G)
  [h : CategoryTheory.Mono f.hom], CategoryTheory.Mono f

This is stated as a lemma to prevent class search from forming a loop since a sheaf morphism is monic if and only if it is monic as a presheaf morphism (under suitable assumption).

Defined in

Mathlib.CategoryTheory.Sites.Sheaf

Cited by

1 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Mono