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Theorems · Definition · category theory

CategoryTheory.IsFiltered.rightToMax

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.IsFilteredOrEmpty C] → (j j' : C) → j' ⟶ CategoryTheory.IsFiltered.max j j'

rightToMax j j' is an arbitrary choice of morphism from j' to max j j', whose existence is ensured by IsFiltered.

Defined in
Mathlib.CategoryTheory.Filtered.Basic
Cited by
26 results in Mathlib
Foundations
Depth 11 from the axioms · uses Classical.choice
Assumes
CategoryTheory.CategoryCategoryTheory.IsFilteredOrEmpty

Around this declaration

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

CategoryTheory.Functor.IsEventuallyConstantFrom.coconeιApp · cited by 4IsEventuallyConstantFrom.…AddMonCat.FilteredColimits.colimit_add_mk_eq · cited by 3FilteredColimits.colimit_…CategoryTheory.IsFilteredOrEmpty.of_right_adjoint · cited by 3IsFilteredOrEmpty.of_righ…CategoryTheory.isFiltered_structuredArrow_of_isFiltered_of_exists · cited by 3CategoryTheory.isFiltered…CategoryTheory.IsFiltered.coeq₃ · cited by 3IsFiltered.coeq₃CategoryTheory.IsFiltered.coeq₃Hom · cited by 3IsFiltered.coeq₃HomCategoryTheory.IsFilteredOrEmpty.of_exists_of_isFiltered_of_fullyFaithful · cited by 3IsFilteredOrEmpty.of_exis…AddMonCat.FilteredColimits.colimit_zero_eq · cited by 2FilteredColimits.colimit_…CategoryTheory.IsFiltered.crown · cited by 2IsFiltered.crownMonCat.FilteredColimits.colimitMulAux · cited by 2FilteredColimits.colimitM…CategoryTheory.ObjectProperty.IsStrongGenerator.isDense_colimitsCardinalClosure_ι · cited by 2IsStrongGenerator.isDense…MonCat.FilteredColimits.colimit_mul_mk_eq · cited by 2FilteredColimits.colimit_…CategoryTheory.Limits.IsColimit.ι_smul · cited by 2IsColimit.ι_smulCategoryTheory.IsFiltered.sup_objs_exists · cited by 2IsFiltered.sup_objs_existsAddMonCat.FilteredColimits.colimitAddAux · cited by 2FilteredColimits.colimitA…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.IsFilteredOrEmpty · cited by 55CategoryTheory.IsFiltered…CategoryTheory.IsFiltered.max · cited by 26IsFiltered.maxIsFiltered.rightToMaxCITED BYCITES

Cites4

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

Cited by34

Results whose statement or proof uses this declaration.