Theorems · Definition · category theory
MonCat.Colimits.coconeMorphism
{J : Type v} →
[inst : CategoryTheory.Category.{u, v} J] →
(F : CategoryTheory.Functor J MonCat) → (j : J) → F.obj j ⟶ MonCat.Colimits.colimit FThe monoid homomorphism from a given monoid in the diagram to the colimit monoid.
- Defined in
- Mathlib.Algebra.Category.MonCat.Colimits
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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 · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- MonCatstatement and proof · cited by 127
- MonCat.ofHomproof · cited by 24
- MonCat.Colimits.colimitstatement · cited by 2
- MonCat.Colimits.coconeFunproof · cited by 0
Cited by3
Results whose statement or proof uses this declaration.
- MonCat.Colimits.cocone_naturalitystatement · cited by 1
- MonCat.Colimits.cocone_naturality_componentsstatement and proof · cited by 0
- MonCat.Colimits.colimitCoconeproof · cited by 0