monoMapFactorizationDataRlp — Mathlib

English

Any monomorphism in a Grothendieck abelian category factors through a generator-connected chain of monomorphisms from G.

Русский

Любой мономорфизм в абелевой категории Гротенштейджа факторизуется через цепь мономорфизмов из G, связанной с порождающей.

LaTeX

$$$f = m_1\\circ m_2\\circ \\cdots$ where each $m_i$ is in generatingMonomorphisms G$$

Lean4

/-- A (functorial) factorization of any morphisms in a Grothendieck abelian category
as a monomorphism followed by a morphism which has the right lifting property
with respect to all monomorphisms. -/
noncomputable abbrev monoMapFactorizationDataRlp {X Y : C} (f : X ⟶ Y) :
    MapFactorizationData (monomorphisms C) (monomorphisms C).rlp f :=
  (functorialFactorizationData _ _).factorizationData f

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