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Theorems · Definition · category theory

MonCat.FilteredColimits.coconeMorphism

{J : Type v} →
  [inst : CategoryTheory.SmallCategory J] →
    (F : CategoryTheory.Functor J MonCat) →
      [inst_1 : CategoryTheory.IsFiltered J] → (j : J) → F.obj j ⟶ MonCat.FilteredColimits.colimit F

The monoid homomorphism from a given monoid in the diagram to the colimit monoid.

Defined in
Mathlib.Algebra.Category.MonCat.FilteredColimits
Cited by
1 results in Mathlib
Foundations
Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.SmallCategoryCategoryTheory.IsFiltered
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MonCat.FilteredColimits.cocone_naturality · cited by 0FilteredColimits.cocone_n…MonCat.FilteredColimits.colimitCocone · cited by 0FilteredColimits.colimitC…DFunLike.coe · cited by 62936DFunLike.coeQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.NatTrans.app · cited by 7406NatTrans.appCategoryTheory.Functor.comp · cited by 6529Functor.compCategoryTheory.ConcreteCategory.hom · cited by 4022ConcreteCategory.homCategoryTheory.Limits.Cocone.ι · cited by 605Cocone.ιCategoryTheory.SmallCategory · cited by 480CategoryTheory.SmallCateg…CategoryTheory.forget · cited by 418CategoryTheory.forgetCategoryTheory.IsFiltered · cited by 210CategoryTheory.IsFilteredMonCat · cited by 127MonCatMonCat.carrier · cited by 107MonCat.carrierMonCat.ofHom · cited by 24MonCat.ofHomCategoryTheory.Limits.Types.TypeMax.colimitCocone · cited by 2TypeMax.colimitCoconeFilteredColimits.coconeMorphi…CITED BYCITES

Cites16

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

Cited by2

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