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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeFeb 6th 2011
• (edited Oct 23rd 2013)

I have started a stub for smooth super infinity-groupoids, with the evident definition and observation that this is cohesive, but nothing else so far. To be worked on. (similar to locally-contractible infinity-groupoid)

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeFeb 6th 2011

I have added a pointer to

• L. Balduzzi, C. Carmeli, R. Fioresi, The local functors of points of Supermanifolds (arXiv:0908.1872)

I am not really sure yet what to make of that article, but it does roughly go in the direction of regarding supermanifolds as sheaves on a combination of smooth manifolds and superpoints (the point here being: if done fully, this would exhibit them as sheaves on an $\infty$-cohesive site).

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeFeb 6th 2011
• (edited Feb 6th 2011)

I have also added the references by Nishimura, who does more explicitly consider the sites $SmoothManifolds \ltimes Superpoints$. However, here too I somewhat still have to make up my mind about what to make of these discussions.

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeOct 23rd 2013
• (edited Oct 23rd 2013)

I have added to smooth super infinity-groupoid some remarks on how it is cohesive over $Super \infty Grpd$ and over $\infty Grpd$.

I have removed the hints that there is an argument for this via externalized internal sites. Once I thought that would be a cool way to say it, but on the one hand it is overkill for what is a simple statement to check directly, and on the other hand I couldn’t in fact quite recall how I thought the argument via internal sites actually works…