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Jeremy Nohel (Dec 19 2025 at 00:18):Hi everyone,
Can anyone suggest any introductory references for simplicial homotopy theory and/or higher categories? My immediate goal is to understand something about 2/bi-/double categories and 2-operads for systems theory, but more broadly I am looking to learn some infinity category theory and related homotopy theory.
As a side note, have people been applying homotopical/infinity-categorical ideas to the sciences at all (more in the spirit of categorical probability, quantum theory, or systems theory as opposed to quantum field theory-related things)?
Kevin Carlson (Dec 19 2025 at 00:27):I don't see a very immediate connection between simplicial homotopy theory or -category theory and 2-dimensional category theory for systems theory, though certainly there exist some more distant relationships. There's a pretty limited amount of -category theory in applied category theory so far. Is there a particular line of work you're hoping to follow?
Jeremy Nohel (Dec 19 2025 at 02:56):Sorry for not being clear enough - my direct interest in applications is for the 2-dimensional theory. The homotopical/infinity-categorical ideas are kind of a separate interest at the moment (though providing motivation for the higher-categorical perspective in general), though I would definitely be interested in following whatever applications may have come up so far. Thanks for the input!
John Baez (Dec 19 2025 at 09:51):We had a discussion comparing introductory texts on simplicial homotopy theory here.
John Baez (Dec 19 2025 at 09:53):Ideas from simplicial homotopy theory are being used quite a lot these days in high-powered quantum field theory.