Theorems · Inductive type · category theory
CategoryTheory.Functor.PreservesMonomorphisms
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
{D : Type u₂} → [inst_1 : CategoryTheory.Category.{v₂, u₂} D] → CategoryTheory.Functor C D → PropA functor preserves monomorphisms if it maps monomorphisms to monomorphisms.
- Defined in
- Mathlib.CategoryTheory.Functor.EpiMono
- Cited by
- 41 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
- CategoryTheory.Functorstatement · cited by 16,252
Cited by46
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.preservesFiniteLimits_tfaeproof · cited by 5
- CategoryTheory.EnoughInjectives.of_adjunctionstatement and proof · cited by 3
- CategoryTheory.Functor.mono_map_iff_monostatement and proof · cited by 3
- CategoryTheory.ObjectProperty.SerreClassLocalization.preservesKernelproof · cited by 3
- CategoryTheory.Functor.preservesHomology_of_map_exactproof · cited by 2
- CategoryTheory.Functor.PreservesMonomorphisms.of_isostatement and proof · cited by 2
- CategoryTheory.Functor.PreservesMonomorphisms.of_natTransstatement and proof · cited by 2
- CategoryTheory.Functor.simple_of_simple_objstatement and proof · cited by 2
- CategoryTheory.ObjectProperty.SerreClassLocalization.preservesMonomorphismsstatement · cited by 2
- CategoryTheory.Limits.colim.map_mono'statement and proof · cited by 2
- CategoryTheory.Adjunction.map_injectivestatement and proof · cited by 2
- CategoryTheory.Functor.preservesHomology_of_preservesMonos_and_cokernelsstatement and proof · cited by 1