Theorems · Theorem · category theory
CategoryTheory.IsFiltered.of_equivalence
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [CategoryTheory.IsFiltered C] {D : Type u₁}
[inst_2 : CategoryTheory.Category.{v₁, u₁} D] (h : C ≌ D), CategoryTheory.IsFiltered DBeing filtered is preserved by equivalence of categories.
- Defined in
- Mathlib.CategoryTheory.Filtered.Basic
- Cited by
- 15 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.
Cites6
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.IsFilteredstatement and proof · cited by 210
- CategoryTheory.Equivalence.symmproof · cited by 195
- CategoryTheory.Equivalence.toAdjunctionproof · cited by 60
- CategoryTheory.IsFiltered.of_right_adjointproof · cited by 2
Cited by15
Results whose statement or proof uses this declaration.
- CategoryTheory.isFiltered_of_isCofiltered_opproof · cited by 3
- CategoryTheory.isCofiltered_costructuredArrow_of_isCofiltered_of_existsproof · cited by 2
- CategoryTheory.AB5OfSize_of_univLEproof · cited by 1
- CategoryTheory.ObjectProperty.of_essentiallySmall_indexproof · cited by 1
- CategoryTheory.isFiltered_of_isFiltered_costructuredArrowproof · cited by 1
- CategoryTheory.Limits.reflectsFilteredColimitsOfSize_of_univLEproof · cited by 1
- CategoryTheory.representablyFlat_op_iffproof · cited by 1
- CategoryTheory.Limits.preservesFilteredColimitsOfSize_of_univLEproof · cited by 1
- CategoryTheory.FinallySmall.exists_of_isFilteredproof · cited by 1
- CategoryTheory.ObjectProperty.ind_indproof · cited by 1
- CategoryTheory.RepresentablyCoflat.of_isoproof · cited by 0