Theorems · Theorem · category theory

CategoryTheory.ObjectProperty.limitsClosure_le

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {P : CategoryTheory.ObjectProperty C} {α : Type t}
  {J : α → Type u'} [inst_1 : (a : α) → CategoryTheory.Category.{v', u'} (J a)] {Q : CategoryTheory.ObjectProperty C}
  [Q.IsClosedUnderIsomorphisms] [∀ (a : α), Q.IsClosedUnderLimitsOfShape (J a)], P ≤ Q → P.limitsClosure J ≤ Q

Defined in

Mathlib.CategoryTheory.ObjectProperty.LimitsClosure

Cited by

6 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.ObjectProperty.IsClosedUnderIsomorphismsCategoryTheory.ObjectProperty.IsClosedUnderLimitsOfShape