Timeline for Can the inner structure of an object be systematically deduced from its position in the category? [closed]
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
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| Jan 4, 2010 at 22:00 | history | closed |
user350 Charles Siegel S. Carnahan♦ Qiaochu Yuan Pete L. Clark |
not a real question | |
| Jan 4, 2010 at 22:00 | comment | added | Pete L. Clark | I'm going to close this up, but please feel free to try again with a more precise, clearly defined question. | |
| Jan 4, 2010 at 18:34 | comment | added | Hans-Peter Stricker | I will follow your advice, that's exactly what I wanted to do next by myself. | |
| Jan 4, 2010 at 17:48 | answer | added | Theo Johnson-Freyd | timeline score: 7 | |
| Jan 4, 2010 at 17:42 | comment | added | S. Carnahan♦ | I'm voting to close. In the future, you may want to ask your vague questions using poset language instead of category language, since counterexamples seem to crop up whenever there is any of the richer structure available to categories (e.g., nonidentity endomorphisms). | |
| Jan 4, 2010 at 17:15 | comment | added | Hans-Peter Stricker | @Joel: Thanks for your advocacy, but to be honest, Reid has captured my intention "better", i.e. that's "precisely" what I meant. (@Reid: You definitely DID guess, what I had in mind, I couldn't - and didn't - have said it better.) | |
| Jan 4, 2010 at 16:46 | comment | added | Reid Barton | @Joel: See, that's the problem--I thought the question was something completely different like "given an object of a category, how/under what conditions on the category can I reconstruct the object (in terms of some external description of the category) from its maps to and from other objects?" | |
| Jan 4, 2010 at 16:23 | comment | added | Joel David Hamkins | Couldn't the question be understood simply as: which categories arise as the category of (small) objects and homomorphisms for a first order theory? Surely many categories arise this way, e.g. groups, rings, etc. and the concept of structure in first order logic is likely the kind of structure that the questioner had in mind. | |
| Jan 4, 2010 at 15:59 | comment | added | Hans-Peter Stricker | Please feel free to close the question (or should I delete it, to keep MO clean?). In order not to bother you with too vague and confusing questions in the future, can you tell me a place where I can clarify my thoughts? (Since there are no official notions of "inner structure" and "position" of objects in a category, category theory textbooks won't help, will they? In introductory/informal texts on category theory instead one often finds these notions mentioned.) | |
| Jan 4, 2010 at 15:33 | comment | added | José Figueroa-O'Farrill | I'm abstaining on closing, but I too find this question very confusing. | |
| Jan 4, 2010 at 15:10 | comment | added | Reid Barton | That said maybe the Yoneda lemma is the answer to your question. | |
| Jan 4, 2010 at 15:09 | comment | added | Reid Barton | I'm voting to close because this question is very vague. I can't guess what you have in mind when you say "inner structure", "systematically deduced", "position in the category". In general there is no notion of "inner structure" of objects in a category. | |
| Jan 4, 2010 at 14:16 | history | asked | Hans-Peter Stricker | CC BY-SA 2.5 |