Theorems · Theorem · category theory

CategoryTheory.Limits.binaryBiconeOfIsSplitEpiOfKernel_fst

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C] {X Y : C} {f : X ⟶ Y}
  [inst_2 : CategoryTheory.IsSplitEpi f] {c : CategoryTheory.Limits.KernelFork f} (i : CategoryTheory.Limits.IsLimit c),
  (CategoryTheory.Limits.binaryBiconeOfIsSplitEpiOfKernel i).fst =
    let c' := CategoryTheory.Limits.KernelFork.ofι (CategoryTheory.Limits.Fork.ι c) ⋯;
    have i' := CategoryTheory.Limits.isKernelCompMono i (CategoryTheory.section_ f) ⋯;
    have i'' := CategoryTheory.Preadditive.isLimitForkOfKernelFork i';
    (CategoryTheory.Limits.splitMonoOfIdempotentOfIsLimitFork C ⋯ i'').retraction

Defined in

Mathlib.CategoryTheory.Preadditive.Biproducts

Cited by

0 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.IsSplitEpi