Theorems · Theorem · category theory
CategoryTheory.Localization.essSurj_mapArrow
∀ {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] (L : CategoryTheory.Functor C D)
(W : CategoryTheory.MorphismProperty C) [L.IsLocalization W] [W.HasLeftCalculusOfFractions], L.mapArrow.EssSurj- Cited by
- 4 results in Mathlib
- Foundations
- Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites38
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.Iso.homproof · cited by 7,684
- CategoryTheory.Iso.invproof · cited by 6,514
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.Isoproof · cited by 3,963
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.Iso.symmproof · cited by 993
Cited by4
Results whose statement or proof uses this declaration.
- CategoryTheory.ObjectProperty.SerreClassLocalization.epi_iffproof · cited by 1
- CategoryTheory.ObjectProperty.SerreClassLocalization.mono_iffproof · cited by 1
- CategoryTheory.Triangulated.Localization.distinguished_cocone_triangleproof · cited by 0