Theorems · Definition · category theory
CategoryTheory.FunctorToTypes.monoFactorisationIsImage
{C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
{F G : CategoryTheory.Functor C (Type u)} →
(f : F ⟶ G) → CategoryTheory.Limits.IsImage (CategoryTheory.FunctorToTypes.monoFactorisation f)The image of a natural transformation between type-valued functors satisfies the universal property of images
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- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
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Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objproof · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.NatTrans.appproof · cited by 7,406
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- TypeCat.ofHomproof · cited by 389
- CategoryTheory.Subfunctor.objproof · cited by 227
- CategoryTheory.Limits.MonoFactorisation.Iproof · cited by 83
- CategoryTheory.Limits.MonoFactorisationproof · cited by 69
- CategoryTheory.Subfunctor.rangeproof · cited by 46
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