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I have a quick lazy question, maybe somebody can point me to the right place in the literature:
The notion of “$\infty$-local systems” as considered in Abad & Schaetz arXiv:1011.4693 and Block & Smith arXiv:0908.2843 are (when over a field of char=0)
probably equivalent to $\infty$-functors from the fundamental $\infty$-groupoid of the domain to the evident $\infty$-category of chain complexes
and probably reflect the $\pi_1$-rational homotopy type of their domain
?
Is this or something like this known/made explicit in the literature anywhere?
Of relevance to this is Lurie, J.. Algebraic K-theory and Manifold Topology, notes for course Math 281 in Autumn 2014. (Lectures 21 and 22), but more importantly Rivera and Zeinalian, https://arxiv.org/abs/1805.01264 in their section 5. Other relevant papers are to be found at Manuel Rivera.
Lurie’s dg-nerve of a dg-category was generalised by Giovanni Faonte in Simplicial nerve of an A∞-category. Theory Appl. Categ 32 (2), (2017) 31 – 52.
Thanks! This article by Rivera & Zeinalian is insightful. I am collecting references at flat infinity-connection.
I alerted Manuel and Mahmoud to your question so hopefully they will contribute some things to the Lab entries. Jim Stasheff and myself have been writing a sort of brief survey on the link between some of these ideas. It should be on the ArXiv soon.
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