Theorems · Theorem · category theory
CategoryTheory.IsFiltered.of_final
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
(F : CategoryTheory.Functor C D) [F.Final] [CategoryTheory.IsFiltered C], CategoryTheory.IsFiltered DFinal functors preserve filteredness.
This can be seen as a generalization of IsFiltered.of_right_adjoint (which states that right
adjoints preserve filteredness), as right adjoints are always final, see final_of_adjunction.
- Defined in
- Mathlib.CategoryTheory.Limits.Final
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 34 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.Functorstatement and proof · cited by 16,252
- CategoryTheory.IsFilteredstatement and proof · cited by 210
- CategoryTheory.Functor.Finalstatement and proof · cited by 112
- CategoryTheory.IsFilteredOrEmptyproof · cited by 55
- CategoryTheory.IsFilteredOrEmpty.of_finalproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.IsIndObject.isFilteredproof · cited by 1
- CategoryTheory.IsCofiltered.of_initialproof · cited by 0