Theorems · Definition · category theory

SemiRingCat.FilteredColimits.colimitCoconeIsColimit.descMonoidHom

{J : Type v} →
  [inst : CategoryTheory.SmallCategory J] →
    {F : CategoryTheory.Functor J SemiRingCat} →
      [inst_1 : CategoryTheory.IsFiltered J] →
        (t : CategoryTheory.Limits.Cocone F) → ↑(SemiRingCat.FilteredColimits.R F) →* ↑t.pt

Auxiliary definition for colimitCoconeIsColimit.

Defined in: Mathlib.Algebra.Category.Ring.FilteredColimits
Cited by: 2 results in Mathlib
Foundations: Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.SmallCategory CategoryTheory.IsFiltered

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Around this declaration

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

Cites17

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

CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.Functor.compproof · cited by 6,529
MonoidHomstatement · cited by 3,629
CategoryTheory.Limits.Cocone.ptstatement · cited by 1,354
CategoryTheory.Limits.Coconestatement and proof · cited by 746
CategoryTheory.SmallCategorystatement and proof · cited by 480
CategoryTheory.forget₂proof · cited by 260
CategoryTheory.IsFilteredstatement and proof · cited by 210
CategoryTheory.Functor.mapCoconeproof · cited by 161
CategoryTheory.Limits.IsColimit.descproof · cited by 144
MonCatproof · cited by 127
MonCat.carrierstatement · cited by 107

Cited by2

Results whose statement or proof uses this declaration.

SemiRingCat.FilteredColimits.colimitCoconeIsColimit.descMonoidHom_quotMkstatement · cited by 1
SemiRingCat.FilteredColimits.colimitCoconeIsColimit.descMonoidHom_apply_eqstatement · cited by 0