Theorems · Theorem · category theory

CategoryTheory.Presheaf.FamilyOfElementsOnObjects.IsCompatible.existsUnique_section

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {J : CategoryTheory.GrothendieckTopology C}
  {F : CategoryTheory.Functor Cᵒᵖ (Type w)} {I : Type u_1} {Y : I → C}
  {x : CategoryTheory.Presheaf.FamilyOfElementsOnObjects F Y},
  x.IsCompatible → J.CoversTop Y → CategoryTheory.Presheaf.IsSheaf J F → ∃! s, ∀ (i : I), ↑s (Opposite.op (Y i)) = x i

Defined in

Mathlib.CategoryTheory.Sites.CoversTop.Basic

Cited by

1 results in Mathlib

Foundations

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

Assumes

CategoryTheory.Category