Theorems · Definition · category theory

CategoryTheory.IsFiltered.toSup

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.IsFiltered C] →
      (O : Finset C) →
        (H : Finset ((X : C) ×' (Y : C) ×' (_ : X ∈ O) ×' (_ : Y ∈ O) ×' (X ⟶ Y))) →
          {X : C} → X ∈ O → (X ⟶ CategoryTheory.IsFiltered.sup O H)

The morphisms to sup O H.

Defined in: Mathlib.CategoryTheory.Filtered.Basic
Cited by: 4 results in Mathlib
Foundations: Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.IsFiltered

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Cites5

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
Finsetstatement and proof · cited by 13,712
CategoryTheory.IsFilteredstatement and proof · cited by 210
CategoryTheory.IsFiltered.supstatement · cited by 4

Cited by4

Results whose statement or proof uses this declaration.

CategoryTheory.IsFiltered.toSup_commutesstatement · cited by 1
CategoryTheory.Limits.Concrete.colimit_no_zero_smul_divisorproof · cited by 0
CategoryTheory.IsFiltered.toSup.congr_simpstatement and proof · cited by 0
CategoryTheory.Limits.colimitLimitToLimitColimit_surjectiveproof · cited by 0