Mathlib Map

Theorems · Definition · category theory

CategoryTheory.Limits.IndObjectPresentation.cocone

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {A : CategoryTheory.Functor Cᵒᵖ (Type v)} →
      (P : CategoryTheory.Limits.IndObjectPresentation A) →
        CategoryTheory.Limits.Cocone (P.F.comp CategoryTheory.yoneda)

The (colimit) cocone with cocone point A.

Defined in
Mathlib.CategoryTheory.Limits.Indization.IndObject
Cited by
8 results in Mathlib
Foundations
Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.Category
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

CategoryTheory.Limits.IndObjectPresentation.toCostructuredArrow · cited by 8IndObjectPresentation.toC…CategoryTheory.Limits.IndObjectPresentation.extend · cited by 6IndObjectPresentation.ext…CategoryTheory.Limits.IndObjectPresentation.coconeIsColimit · cited by 2IndObjectPresentation.coc…CategoryTheory.Limits.IndizationClosedUnderFilteredColimitsAux.isFiltered · cited by 1IndizationClosedUnderFilt…CategoryTheory.Limits.IndObjectPresentation.extend_ι_app_app_hom_apply · cited by 0IndObjectPresentation.ext…CategoryTheory.Limits.IndObjectPresentation.toCostructuredArrow_map_left · cited by 0IndObjectPresentation.toC…CategoryTheory.Limits.IndObjectPresentation.toCostructuredArrow_obj_hom · cited by 0IndObjectPresentation.toC…CategoryTheory.NonemptyParallelPairPresentationAux.hg · cited by 0NonemptyParallelPairPrese…CategoryTheory.Limits.IndObjectPresentation.cocone_pt · cited by 0IndObjectPresentation.coc…CategoryTheory.NonemptyParallelPairPresentationAux.hf · cited by 0NonemptyParallelPairPrese…CategoryTheory.Limits.IndObjectPresentation.extend_isColimit_desc_app_hom_apply · cited by 0IndObjectPresentation.ext…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorOpposite · cited by 8081OppositeCategoryTheory.Functor.comp · cited by 6529Functor.compCategoryTheory.Limits.Cocone · cited by 746Limits.CoconeCategoryTheory.yoneda · cited by 351CategoryTheory.yonedaCategoryTheory.Limits.IndObjectPresentation · cited by 20Limits.IndObjectPresentat…CategoryTheory.Limits.IndObjectPresentation.I · cited by 18IndObjectPresentation.ICategoryTheory.Limits.IndObjectPresentation.F · cited by 12IndObjectPresentation.FCategoryTheory.Limits.IndObjectPresentation.ℐ · cited by 11IndObjectPresentation.ℐCategoryTheory.Limits.IndObjectPresentation.ι · cited by 3IndObjectPresentation.ιIndObjectPresentation.coconeCITED BYCITES

Cites11

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

Cited by11

Results whose statement or proof uses this declaration.