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I thought I'd amuse myself with creating a succinct list of all the useful structures that we have canonically in an (oo,1)-topos without any intervention by hand:
I started typing that at structures in a gros (oo,1)-topos on my personal web.
I think this gives a quite remarkable story of pure abstract nonsense. None of this is created "by man" in a way. It all just exists.
Certainly my list needs lots of improvements. But I am too tired now. I thought I'd share this anyway now. Comments are welcome.
Main point missing in the list currently is the free loop space object, Hochschild cohomology and Domenico's proposal to define the Chern character along that route. I am still puzzled by how exactly the derived loop space should interact with and .
expanded my collection of canonical structurs in an (oo1,)-topos a bit further
have been further expanding and streamlining formal structures in an (oo,1)-topos.
Find it quite pleasing what a whealth of structures comes out for free here.
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