cokernelBiproductFromSubtypeIso — Mathlib

English

There is a canonical cokernel iso as described earlier; the cokernel of biproduct.fromSubtype f p is the biproduct of Subtype.restrict pᶜ f.

Русский

Существует каноническое коконечерное изоморфизм: коконцеп Biprodut.fromSubtype f p эквивалентен биопродукту Subtype.restrict pᶜ f.

LaTeX

$$$\\text{cokernel}(\\text{biproduct.fromSubtype } f p) \\cong ⨁ \\text{Subtype.restrict } p^c f$$$

Lean4

/-- The cokernel of `biproduct.fromSubtype f p` is `⨁ Subtype.restrict pᶜ f`. -/
@[simps!]
def cokernelBiproductFromSubtypeIso (p : Set K) : cokernel (biproduct.fromSubtype f p) ≅ ⨁ Subtype.restrict pᶜ f :=
  colimit.isoColimitCocone (cokernelCoforkBiproductFromSubtype f p)

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