Theorems · Definition · category theory

CategoryTheory.Subobject.factorThru

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {X Y : C} →
      (P : CategoryTheory.Subobject Y) → (f : X ⟶ Y) → P.Factors f → (X ⟶ CategoryTheory.Subobject.underlying.obj P)

P.factorThru f h provides a factorisation of f : X ⟶ Y through some P : Subobject Y, given the evidence h : P.Factors f that such a factorisation exists.

Defined in

Mathlib.CategoryTheory.Subobject.FactorThru

Cited by

35 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category