Theorems · Theorem · category theory
CategoryTheory.IsCofilteredOrEmpty.of_equivalence
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [CategoryTheory.IsCofilteredOrEmpty C] {D : Type u₁}
[inst_2 : CategoryTheory.Category.{v₁, u₁} D] (h : C ≌ D), CategoryTheory.IsCofilteredOrEmpty DBeing cofiltered or empty is preserved by equivalence of categories.
- Defined in
- Mathlib.CategoryTheory.Filtered.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.Equivalencestatement and proof · cited by 601
- CategoryTheory.Equivalence.toAdjunctionproof · cited by 60
- CategoryTheory.IsCofilteredOrEmptystatement and proof · cited by 55
- CategoryTheory.IsCofilteredOrEmpty.of_left_adjointproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.isCofilteredOrEmpty_of_isFilteredOrEmpty_opproof · cited by 2