Theorems · Definition · category theory

CategoryTheory.SmallObject.functorialFactorizationData

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    (I : CategoryTheory.MorphismProperty C) →
      (κ : Cardinal.{w}) →
        [inst_1 : Fact κ.IsRegular] →
          [inst_2 : OrderBot κ.ord.ToType] →
            [I.IsCardinalForSmallObjectArgument κ] → I.rlp.llp.FunctorialFactorizationData I.rlp

The functorial factorization ιObj I κ f ≫ πObj I κ f.hom = f with ιObj I κ f in I.rlp.llp and πObj I κ f.hom in I.rlp.

Defined in

Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument

Cited by

5 results in Mathlib

Foundations

Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryFactOrderBotCategoryTheory.MorphismProperty.IsCardinalForSmallObjectArgument