Theorems · Theorem · category theory
CategoryTheory.IsCofiltered.of_equivalence
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [CategoryTheory.IsCofiltered C] {D : Type u₁}
[inst_2 : CategoryTheory.Category.{v₁, u₁} D] (h : C ≌ D), CategoryTheory.IsCofiltered DBeing cofiltered is preserved by equivalence of categories.
- Defined in
- Mathlib.CategoryTheory.Filtered.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 30 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.IsCofilteredstatement and proof · cited by 133
- CategoryTheory.Equivalence.toAdjunctionproof · cited by 60
- CategoryTheory.IsCofiltered.of_left_adjointproof · cited by 2
Cited by10
Results whose statement or proof uses this declaration.
- CategoryTheory.isCofiltered_of_isFiltered_opproof · cited by 6
- CategoryTheory.AB5StarOfSize_of_univLEproof · cited by 1
- CategoryTheory.representablyFlat_op_iffproof · cited by 1
- CategoryTheory.Limits.preservesCofilteredLimitsOfSize_of_univLEproof · cited by 1
- CategoryTheory.Limits.reflectsCofilteredLimitsOfSize_of_univLEproof · cited by 1
- CategoryTheory.IsCofiltered.iff_of_equivalenceproof · cited by 0
- CategoryTheory.Comma.final_snd_of_isFiltered_structuredArrowproof · cited by 0
- CategoryTheory.representablyCoflat_op_iffproof · cited by 0
- CategoryTheory.RepresentablyFlat.of_isoproof · cited by 0
- CategoryTheory.Comma.isFiltered_of_isFiltered_structuredArrowproof · cited by 0