Theorems · Definition · category theory
CategoryTheory.section_
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] → {X Y : C} → (f : X ⟶ Y) → [hf : CategoryTheory.IsSplitEpi f] → Y ⟶ XThe chosen section of a split epimorphism.
(Note that section is a reserved keyword, so we append an underscore.)
- Defined in
- Mathlib.CategoryTheory.EpiMono
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses Classical.choice
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
- Quiver.Homstatement and proof · cited by 32,603
- Nonempty.someproof · cited by 340
- CategoryTheory.IsSplitEpistatement and proof · cited by 46
- CategoryTheory.SplitEpi.section_proof · cited by 22
- CategoryTheory.IsSplitEpi.exists_splitEpiproof · cited by 4
Cited by26
Results whose statement or proof uses this declaration.
- CategoryTheory.IsSplitEpi.idstatement · cited by 12
- CategoryTheory.Limits.binaryBiconeOfIsSplitEpiOfKernelproof · cited by 5
- SSet.Subcomplex.mem_degenerate_iffproof · cited by 5
- CategoryTheory.isIso_of_mono_of_isSplitEpiproof · cited by 4
- CategoryTheory.Limits.coconeOfIsSplitEpistatement · cited by 3
- CategoryTheory.Sieve.generate_of_contains_isSplitEpiproof · cited by 3
- SSet.S.existsUnique_nproof · cited by 2
- CategoryTheory.Pretriangulated.exists_iso_binaryBiproduct_of_distTriangproof · cited by 1
- CategoryTheory.section_.congr_simpstatement and proof · cited by 1
- SSet.S.subcomplex_eq_of_epiproof · cited by 1
- CategoryTheory.Abelian.has_injective_coseparatorproof · cited by 1
- SSet.Subcomplex.ofSimplex_map_of_epiproof · cited by 1