Theorems · Theorem · category theory
CategoryTheory.section_.congr_simp
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y : C} (f f_1 : X ⟶ Y) (e_f : f = f_1)
[hf : CategoryTheory.IsSplitEpi f], CategoryTheory.section_ f = CategoryTheory.section_ f_1- Defined in
- Mathlib.CategoryTheory.EpiMono
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses Classical.choice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- CategoryTheory.IsSplitEpistatement and proof · cited by 46
- CategoryTheory.section_statement and proof · cited by 21
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.IsZero.iff_isSplitEpi_eq_zeroproof · cited by 1