Theorems · Inductive type · category theory
CategoryTheory.IsSplitEpi
{C : Type u₁} → [inst : CategoryTheory.Category.{v₁, u₁} C] → {X Y : C} → (X ⟶ Y) → PropIsSplitEpi f is the assertion that f admits a section
- Defined in
- Mathlib.CategoryTheory.EpiMono
- Cited by
- 46 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
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
- Quiver.Homstatement · cited by 32,603
Cited by58
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.exact_of_f_is_kernelproof · cited by 22
- CategoryTheory.section_statement and proof · cited by 21
- CategoryTheory.IsSplitEpi.idstatement and proof · cited by 12
- CategoryTheory.isSplitEpi_of_epistatement · cited by 9
- CategoryTheory.IsSplitEpi.casesOnstatement and proof · cited by 5
- CategoryTheory.IsSplitEpi.mk'statement · cited by 5
- CategoryTheory.Limits.binaryBiconeOfIsSplitEpiOfKernelstatement and proof · cited by 5
- SSet.Subcomplex.mem_degenerate_iffproof · cited by 5
- CategoryTheory.isIso_of_mono_of_isSplitEpistatement and proof · cited by 4
- CategoryTheory.IsSplitEpi.exists_splitEpistatement and proof · cited by 4
- CategoryTheory.Limits.coconeOfIsSplitEpistatement and proof · cited by 3
- CategoryTheory.Abelian.epiWithInjectiveKernel_iffproof · cited by 3