Theorems · Definition · category theory

CategoryTheory.IsFiltered.SmallFilteredIntermediate.factoringCompInclusion

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.IsFilteredOrEmpty C] →
      {D : Type u₁} →
        [inst_2 : CategoryTheory.Category.{v₁, u₁} D] →
          (F : CategoryTheory.Functor D C) →
            (CategoryTheory.IsFiltered.SmallFilteredIntermediate.factoring F).comp
                (CategoryTheory.IsFiltered.SmallFilteredIntermediate.inclusion F) ≅
              F

The factorization through a small filtered category is in fact a factorization, up to natural isomorphism.

Defined in

Mathlib.CategoryTheory.Filtered.Small

Cited by

1 results in Mathlib

Foundations

Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.IsFilteredOrEmptyCategoryTheory.Category