Theorems · Theorem · category theory
CategoryTheory.Functor.reflects_precoherent
∀ {C : Type u_1} {D : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C]
[inst_1 : CategoryTheory.Category.{v_2, u_2} D] (F : CategoryTheory.Functor C D)
[F.PreservesFiniteEffectiveEpiFamilies] [F.ReflectsFiniteEffectiveEpiFamilies] [F.EffectivelyEnough]
[CategoryTheory.Precoherent D] [F.Full] [F.Faithful], CategoryTheory.Precoherent C- Cited by
- 3 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
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
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functor.objproof · cited by 19,642
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapproof · cited by 8,698
- CategoryTheory.Category.assocproof · cited by 6,433
- Finiteproof · cited by 3,029
- CategoryTheory.Functor.map_compproof · cited by 734
- CategoryTheory.Functor.Fullstatement and proof · cited by 341
- Nonempty.someproof · cited by 340
- CategoryTheory.Functor.Faithfulstatement and proof · cited by 313
Cited by5
Results whose statement or proof uses this declaration.
- CategoryTheory.Equivalence.precoherentproof · cited by 11
- CategoryTheory.coherentTopology.coverPreservingstatement · cited by 0
- CategoryTheory.coherentTopology.eq_inducedstatement and proof · cited by 0
- CategoryTheory.coherentTopology.equivalencestatement · cited by 0
- CategoryTheory.coherentTopology.equivalence'statement · cited by 0