Theorems · Definition · category theory

CategoryTheory.FunctorToTypes.monoFactorisation

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    {F G : CategoryTheory.Functor C (Type u)} → (f : F ⟶ G) → CategoryTheory.Limits.MonoFactorisation f

The image of a natural transformation between type-valued functors is a MonoFactorisation

Defined in: Mathlib.CategoryTheory.Limits.FunctorCategory.Shapes.Images
Cited by: 3 results in Mathlib
Foundations: Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

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Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.Subfunctor.toFunctorproof · cited by 90
CategoryTheory.Limits.MonoFactorisationstatement · cited by 69
CategoryTheory.Subfunctor.ιproof · cited by 50
CategoryTheory.Subfunctor.rangeproof · cited by 46
CategoryTheory.Subfunctor.toRangeproof · cited by 10

Cited by4

Results whose statement or proof uses this declaration.

CategoryTheory.FunctorToTypes.monoFactorisation_estatement and proof · cited by 0
CategoryTheory.FunctorToTypes.monoFactorisation_mstatement and proof · cited by 0
CategoryTheory.FunctorToTypes.monoFactorisationIsImagestatement and proof · cited by 0
CategoryTheory.FunctorToTypes.monoFactorisation_Istatement and proof · cited by 0