Theorems · Theorem · category theory
MonCat.Colimits.cocone_naturality
∀ {J : Type v} [inst : CategoryTheory.Category.{u, v} J] (F : CategoryTheory.Functor J MonCat) {j j' : J} (f : j ⟶ j'),
CategoryTheory.CategoryStruct.comp (F.map f) (MonCat.Colimits.coconeMorphism F j') =
MonCat.Colimits.coconeMorphism F j- Defined in
- Mathlib.Algebra.Category.MonCat.Colimits
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapstatement · cited by 8,698
- MonCatstatement and proof · cited by 127
- MonoidHom.extproof · cited by 109
- MonCat.carrierproof · cited by 107
- MonCat.Colimits.coconeMorphismstatement · cited by 2
- MonCat.Colimits.colimitstatement · cited by 2
- MonCat.hom_extproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- MonCat.Colimits.cocone_naturality_componentsproof · cited by 0