From: Noah Snyder <nsnyder@gmail.com> To: Homotopy Type Theory <HomotopyTypeTheory@googlegroups.com> Subject: [HoTT] Dependent path composition in ordinary higher category theory Date: Fri, 28 Feb 2020 10:33:58 -0800 Message-ID: <CAO0tDg7uSiQrU8+0tnwJQHB_AWvRKAxmAePF88GOvd_ra=rpwA@mail.gmail.com> (raw) [-- Attachment #1: Type: text/plain, Size: 1698 bytes --] Section 2.3 of the book introduces "dependent paths" (which are paths in a fibration "lying over" a path in the base) and "dependent path composition" which composes such dependent paths when that makes sense. I'm working on a paper that's not about HoTT but where "dependent path composition" plays an important role. The problem I'm running into is that I don't know what dependent path composition is called in "standard" mathematics. Does anyone know if this has another name in higher category theory? (Naturally, we'll include a remark mentioning the HoTT way of thinking about this (since it's how I think about it!), but I think that won't be illuminating to most of our target audience.) The simplest example of what I have in mind here is if C is a category and F is an endofunctor and c is an F-algebra (i.e. we have endowed c with a chosen map f: F(c) --> c) then c is also an F^n-algebra by taking the "nth power of f" which actually means f \circ F(f) \circ F^2(f) \circ ... \circ F^{n-1}(f). In particular, I think this example illustrates that you can talk about "dependent k-morphisms" and their compositions without requiring anything in sight to be a (higher) groupoid. My best guess is that the right setting might be "indexed (higher) categories"? Best, Noah -- You received this message because you are subscribed to the Google Groups "Homotopy Type Theory" group. To unsubscribe from this group and stop receiving emails from it, send an email to HomotopyTypeTheory+unsubscribe@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/HomotopyTypeTheory/CAO0tDg7uSiQrU8%2B0tnwJQHB_AWvRKAxmAePF88GOvd_ra%3DrpwA%40mail.gmail.com. [-- Attachment #2: Type: text/html, Size: 2226 bytes --]

next reply indexThread overview:3+ messages / expand[flat|nested] mbox.gz Atom feed top2020-02-28 18:33 Noah Snyder [this message]2020-02-28 18:44 ` [HoTT] " Noah Snyder 2020-03-02 7:03 ` Michael Shulman

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