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code style fix
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s3midetnov committed Jun 19, 2024
1 parent ceaa12a commit 0534f12
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Showing 2 changed files with 5 additions and 4 deletions.
8 changes: 4 additions & 4 deletions src/Algebra/Group/GSet/Category.ard
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Expand Up @@ -11,22 +11,22 @@
\import Set
\import Set.Category

\record EquivariantMaps (G : Group) \extends SetHom{
\record EquivariantMap (G : Group) \extends SetHom{
\override Dom : GroupAction G
\override Cod : GroupAction G
| func-** {e : Dom} {g : G} : func (g ** e) = g ** func e -- equivariance

\func isIso => \Sigma (isSurj func) (isInj func)
}

\func id-equivar {G : Group} (X : GroupAction G) : EquivariantMaps G { | Dom => X | Cod => X} \cowith
\func id-equivar {G : Group} (X : GroupAction G) : EquivariantMap G { | Dom => X | Cod => X} \cowith
| func (x : X) => x
| func-** {x : X} {g : G} => idp

\instance GSet (G : Group) : Cat (GroupAction G)
| Hom A B => EquivariantMaps G { | Dom => A | Cod => B}
| Hom A B => EquivariantMap G { | Dom => A | Cod => B}
| id X => id-equivar X
| o {x y z : GroupAction G} (g : EquivariantMaps G y z) (f : EquivariantMaps G x y) => \new EquivariantMaps G {
| o {x y z : GroupAction G} (g : EquivariantMap G y z) (f : EquivariantMap G x y) => \new EquivariantMap G {
| func (a : x) => g (f a)
| func-** {a : x} {h : G} =>
g ( f (h ** a)) ==< pmap g func-** >==
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1 change: 1 addition & 0 deletions src/Algebra/Group/GSet/GSet.ard
Original file line number Diff line number Diff line change
Expand Up @@ -82,6 +82,7 @@
)
}

-- action by conjugating its own elements
\func conjAction (G : Group) : GroupAction G \cowith
| E => G
| ** (g : G) => conjugate g
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