Theorems · Definition · category theory

CategoryTheory.Sheaf.classifier

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    (J : CategoryTheory.GrothendieckTopology C) →
      CategoryTheory.Subobject.Classifier (CategoryTheory.Sheaf J (Type (max u v)))

A construction of a subobject classifier for sheaf categories. Ω is the sheaf of closed sieves, and truth maps for each object X : C, an element of PUnit to the maximal Sieve X, which is always closed.

Defined in

Mathlib.CategoryTheory.Topos.Sheaf

Cited by

5 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category