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Theorems · Definition · group theory

Rep.ActionToRep

(k : Type u) →
  (G : Type v) →
    [inst : Ring k] → [inst_1 : Monoid G] → CategoryTheory.Functor (Action (ModuleCat k) G) (Rep.{w, u, v} k G)

Every object in ModuleCat k that G acts on is an object in Rep k G.

Defined in
Mathlib.RepresentationTheory.Rep.Basic
Cited by
3 results in Mathlib
Foundations
Depth 54 from the axioms · uses propext, Quot.sound
Assumes
RingMonoid
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Around this declaration

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

Rep.ActionToRep_RepToAction · cited by 0Rep.ActionToRep_RepToActi…Rep.ActionToRep_map · cited by 0Rep.ActionToRep_mapRep.ActionToRep_obj_V · cited by 0Rep.ActionToRep_obj_VRep.ActionToRep_obj_ρ · cited by 0Rep.ActionToRep_obj_ρRep.repIsoAction · cited by 0Rep.repIsoActionRep.RepToAction_ActionToRep · cited by 0Rep.RepToAction_ActionToR…Quiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorRing · cited by 7463RingMonoid · cited by 3887MonoidModuleCat · cited by 1429ModuleCatRep · cited by 843RepMonoidHom.comp · cited by 469MonoidHom.compModuleCat.Hom.hom · cited by 341Hom.homAction · cited by 206ActionAction.V · cited by 176Action.VAction.Hom.hom · cited by 86Hom.homRep.of · cited by 57Rep.ofAction.ρ · cited by 51Action.ρRep.ofHom · cited by 45Rep.ofHomRingEquiv.toMonoidHom · cited by 13RingEquiv.toMonoidHomRep.ActionToRepCITED BYCITES

Cites16

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

Cited by6

Results whose statement or proof uses this declaration.