Timeline for Studying higher categories from the bottom up
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Dec 14, 2020 at 20:05 | comment | added | Alec Rhea | That's interesting, I'll take a closer look at the globular approach. (I'd also be interested in looking at the Riehl/Verity work) One method of reducing the diagram work taken by Mike Shulman is to rely on the internal logic of higher categories to express diagrams using set-theory like notation in the internal language, with some nice results. | |
| Dec 14, 2020 at 19:06 | comment | added | Mozibur Ullah | @Alec Rhea: I think the globular approach is considered an algebraic approach - at least according to Nlab - but there's still some work to go. | |
| Dec 14, 2020 at 19:02 | comment | added | Mozibur Ullah | @Alec Rhea: In that case can I just say ZFC :-)? I know exactly what you mean. I heard about the intimidating definition of Trimbles tetracategories probably from the same source years ago. Luckily, Trimble says that his approach is 'primative' and hence recognises the need for more sophistication to bring down the diagram count. There are other approaches - Emily Riehl & Dominic Verity are attempting a model independebt approach whilst the homotopy type approach sell themselves as infinity categories for undergraduates. I'll wait & see ;-). | |
| Dec 14, 2020 at 18:56 | comment | added | Alec Rhea | I am (vaguely) aware that there are various models for $\infty$-categories, but I prefer algebraic definitions and it's still in the air what an algebraic definition of a fully weak infinity category should be. | |
| Dec 14, 2020 at 18:53 | comment | added | Alec Rhea | Extensionality, regularity, comprehension, infinity, powerset, pairing, union, replacement, choice if you like. (I didn't see your answer till about a minute ago ;). More seriously though, my point is that even if you have the definition sitting right next to you, the time it takes to copy it down (let alone digest it) increases superexponentially past the bicategorical level, to the point where just writing down the algebraic definition of a tetracategory is intimidating (see Todd Trimbles notes for an example, it takes 51 pages: math.ucr.edu/home/baez/trimble/tetracategories.html) | |
| Dec 14, 2020 at 18:44 | history | answered | Mozibur Ullah | CC BY-SA 4.0 |