Theorems · Theorem · category theory

TopCat.isOpen_iff_of_isColimit

∀ {J : Type v} [inst : CategoryTheory.Category.{w, v} J] {F : CategoryTheory.Functor J TopCat}
  (c : CategoryTheory.Limits.Cocone F) (hc : CategoryTheory.Limits.IsColimit c) (X : Set ↑c.pt),
  IsOpen X ↔ ∀ (j : J), IsOpen (⇑(CategoryTheory.ConcreteCategory.hom (c.ι.app j)) ⁻¹' X)

Defined in

Mathlib.Topology.Category.TopCat.Limits.Basic

Cited by

4 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category