Tensor product of left exact morphisms

[Richard Garner <richard.garner@mq.edu.au>]

Dear categorists,

If G is a group, then [G,Set] is the classifying topos for right
G-torsors.

What about the classifying topos for possibly non-transitive torsors?

I'm not very adept at these calculations, but if I construct it as a
subtopos of the classifying topos for G^op-sets, it appears to come out
as [X,Set] where X is the category of finitely presentable, free,
non-empty G^op-sets.

Similarly, if G is a groupoid, the corresponding classifying topos
appears to be [X,Set], where X is the full subcategory of [G^op, Set] on
those finite coproducts of representables which have global support.

Is this correct?

Richard


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