Theorems · Theorem · category theory

CategoryTheory.Regular.exists_inf_pullback_eq_exists_inf

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Regular C] {A B : C} (f : A ⟶ B)
  (A' : CategoryTheory.Subobject A) (B' : CategoryTheory.Subobject B),
  (CategoryTheory.Subobject.exists f).obj (A' ⊓ (CategoryTheory.Subobject.pullback f).obj B') =
    (CategoryTheory.Subobject.exists f).obj A' ⊓ B'

Regular categories satisfy Frobenius reciprocity. That is, in the internal language of regular categories, we have ∃ x, (P(x) ⊓ Q) iff (∃ x, P(x)) ⊓ Q, for a proposition Q not depending on x.

Defined in

Mathlib.CategoryTheory.RegularCategory.Basic

Cited by

0 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Regular