WikiLeanRecent changes · Proposals · Flags · Stats · About

Diff — Group action

Revision #1277 → #2287 · back to history

addedCayley's theoremc85ae5ad2cee
modifiedSemisimple action3ee25c6b77dd
FieldFrom #1277To #2287
mathlib.declIsSemisimpleRepresentationRepresentation.IsSemisimpleRepresentation
note`IsSemisimpleRepresentation` (equiv. `IsSemisimpleModule` over `k[G]`) is the semisimplicity of a linear action.`Representation.IsSemisimpleRepresentation ρ` (equivalent to `IsSemisimpleModule` over `MonoidAlgebra k G`) is the semisimplicity of a linear action.
addedKernel of action equals intersection of stabilizers4db33c37e8bd
modifiedCategory of G-sets398a7ba11287
FieldFrom #1277To #2287
mathlib.declCategoryTheory.ActionAction
note`Action (Type u) G` is the category of G-sets (the docstring notes `V = Type` gives G-actions).`Action (Type u) G` is the category of G-sets (specializing the general `Action V G` structure to `V = Type u`).
modifiedAction groupoid4198f868bafc
FieldFrom #1277To #2287
note`CategoryTheory.ActionCategory M X` is the action groupoid (groupoid when `M` is a group).`CategoryTheory.ActionCategory M X` is the action groupoid (a groupoid when `M` is a group).
modifiedG-sets form a Grothendieck toposae9878fa8096
FieldFrom #1277To #2287
mathlib.declCategoryTheory.ActionAction
modifiedActions on objects of a categorycf85ae469760
FieldFrom #1277To #2287
mathlib.declCategoryTheory.ActionAction