AG theory with syntactic category = k[x]-modules ... vs Z-graded k[x]-modules .... ???? ...

semantic :

g-torsor x

g-torsor x equipped with point y in f(x)

framed g-torsor x equipped with point y in f(x)


syntactic :

g-rep ...

?? g-action on (r,m) extending given g-action on r .... ???? .....

r-module m ... ?? ....

????? ...... ????? ....