Timeline for Why do we need filtered categories to index ind-objects?
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Jul 10, 2015 at 5:59 | comment | added | Tyler Lawson | There is also some discussion of this early in Adámek and Rosicky's book "Locally presentable and accessible categories" (the section on directed and filtered colimits). | |
| Jul 10, 2015 at 5:44 | answer | added | Dylan Wilson | timeline score: 6 | |
| Jul 10, 2015 at 3:58 | history | edited | category_student | CC BY-SA 3.0 |
added 8 characters in body; edited title
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| Jul 10, 2015 at 3:51 | comment | added | category_student | OK, thanks, it was not clear to me that this was a cardinality issue. A last question: Can I always index an ind-object by an ordinal, instead of just the integers? | |
| Jul 10, 2015 at 1:23 | comment | added | David Roberts♦ | @EricWofsey well, assuming appropriate background logic :-) | |
| Jul 10, 2015 at 0:58 | comment | added | Benjamin Steinberg | It's like sequences versus nets. | |
| Jul 10, 2015 at 0:48 | comment | added | Eric Wofsey | For countable filtered diagrams, you can always find a cofinal sequence, but for uncountable filtered diagrams you usually cannot. | |
| Jul 10, 2015 at 0:40 | comment | added | grghxy | Please describe $\mathbf{C}$ as a direct limit of a countably-indexed directed system of finitely generated $\mathbf{Q}$-subalgebras. Lots of interesting "ind"-constructions cannot be expressed with a countable index set. | |
| Jul 10, 2015 at 0:33 | comment | added | category_student | OK but given an ind-object indexed by integers with divisibility I can just look at $n!$ and get an equivalent ind-object indexed by integers. Can I always do that? | |
| Jul 10, 2015 at 0:24 | history | made wiki | Post Made Community Wiki by Todd Trimble | ||
| Jul 10, 2015 at 0:21 | comment | added | David Roberts♦ | Positive integers with the divisibility order. | |
| Jul 10, 2015 at 0:08 | history | edited | category_student | CC BY-SA 3.0 |
edited title
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| Jul 10, 2015 at 0:04 | review | First posts | |||
| Jul 10, 2015 at 0:33 | |||||
| Jul 10, 2015 at 0:03 | history | asked | category_student | CC BY-SA 3.0 |