Timeline for Are there substantive differences between the different approaches to "size issues" in category theory?
Current License: CC BY-SA 4.0
Post Revisions
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 26, 2024 at 22:07 | comment | added | Alec Rhea | @DenisT You do not encounter anything? Sounds like a boring life! ;^) | |
| Jun 26, 2024 at 11:40 | comment | added | Denis T | @AlecRhea I do not "encounter" anything, I just know that accessible categories do not form a category in any meaningful way. If you have some magical way to define morphism sets between accessible categories of unbounded accessibility rank, I'll be very interested to know. | |
| Jun 26, 2024 at 8:03 | vote | accept | Joe Lamond | ||
| Jun 24, 2024 at 20:24 | history | became hot network question | |||
| Jun 24, 2024 at 20:08 | answer | added | Joel David Hamkins | timeline score: 18 | |
| Jun 24, 2024 at 20:04 | comment | added | Alec Rhea | @DenisT I'm not sure what you mean by 'rarely exist'; perhaps you mean that you don't encounter them 'in nature' in your own work, which is fine. I do, and for me functors not forming a category is pretty much always a bug, but to each their own :^). | |
| Jun 24, 2024 at 18:01 | answer | added | Simon Henry | timeline score: 22 | |
| Jun 24, 2024 at 13:28 | answer | added | Alec Rhea | timeline score: 9 | |
| Jun 24, 2024 at 13:18 | comment | added | Denis T | @AlecRhea Functors not forming a category is not a bug, it is a feature. | |
| Jun 24, 2024 at 13:15 | comment | added | Denis T | Functor categories rarely exist without restrictions on the nature of functors, if the domain of big. If you work with universes, you'll get a lot of "fake" functor categories; metaphorically speaking, you'll get something like a subring of $End(V)$ for a vector space of cardinality $a$, such that rank of the image has cardinality at most $b$. It's much more natural and less error-prone to impose those restrictions on "size of functors" explicitly. | |
| Jun 24, 2024 at 13:13 | comment | added | Emil Jeřábek | Rank isn’t invariant under isomorphism, but cardinality is. | |
| Jun 24, 2024 at 13:08 | comment | added | Alec Rhea | Taking the classes view presents naïve issues with things like functor categories between large categories etc., since you’ll want a category whose objects are proper classes which is impossible in e.g. MK class theory. | |
| Jun 24, 2024 at 12:24 | history | asked | Joe Lamond | CC BY-SA 4.0 |