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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeSep 18th 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexI 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](https://arxiv.org/abs/1011.4693) and Block & Smith [arXiv:0908.2843](https://arxiv.org/abs/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?

   I have a quick lazy question, maybe somebody can point me to the right place in the literature:

   The notion of “-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 -functors from the fundamental -groupoid of the domain to the evident -category of chain complexes

   • and probably reflect the -rational homotopy type of their domain

   ?

   Is this or something like this known/made explicit in the literature anywhere?

2. • CommentRowNumber2.
   • CommentAuthorTim_Porter
   • CommentTimeSep 19th 2022
   • (edited Sep 19th 2022)
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownItexOf 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.

   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.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeSep 20th 2022
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   Author: Urs
   Format: MarkdownItexThanks! This article by Rivera & Zeinalian is insightful. I am collecting references at *[[flat infinity-connection]]*.

   Thanks! This article by Rivera & Zeinalian is insightful. I am collecting references at flat infinity-connection.

4. • CommentRowNumber4.
   • CommentAuthorTim_Porter
   • CommentTimeSep 20th 2022
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownItexI 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.

   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.