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Adittya Chaudhuri (Mar 15 2025 at 17:50):I apologise priorly, if my question sounds a little vague. But I am searching for the right mathematical language to describe it.
Say, a game(like Soccer) is being played among teams (unlike =2 as the usual case) in a huge play ground. A collection of audiances is watching and trying to analyse the game. Now, the audiance is seeing interaction among players (both intra and inter teams). Now, in a way after watching the game for a "sufficient period of time", audiances started making statements about "how each team interacts with other teams" (zooming out from the level of players). I am thinking of this analysis as an "emergence of collection level interactions" from a "family of individual level interactions".
Now, if we represent the "player level interactions"as a labeled directed graph , then the induced collection level interaction would be labeled directed hypergraph. I was thinking of a functorial (functorial upto certain factors) relationships between labeled directed graphs and labeled directed hypergraphs to describe "this sort of transition from individual interactions to collection level interactions".
Has there been any existing study in this direction? What could be a right mathematicial language to study such interactions?
I was also vaguely thinking about sheaves/stacks (if we want to relax the locally determined condition)-but not sure!!
Thanks in advance.
Morgan Rogers (he/him) (Mar 17 2025 at 08:25):Concepts from "coarse geometry", which I learned about in a course on geometric group theory, come to mind. Roughly (unapologetic pun) the idea is to capture when things 'look the same from far away'
Adittya Chaudhuri (Mar 17 2025 at 09:57):Interesting! Thank you @Morgan Rogers (he/him) . I am not familiar with this area of geometry. I will look into it.