Timeline for Do hom-sets really live in the category Set?
Current License: CC BY-SA 3.0
11 events
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| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
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| Apr 8, 2015 at 4:17 | comment | added | Martin Brandenburg | I just wanted to remark that I've posted an answer on the math.SE version of this question. | |
| Jan 22, 2015 at 14:56 | history | edited | Todd Trimble | CC BY-SA 3.0 |
added a link to the M.SE question
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| Jan 22, 2015 at 14:44 | comment | added | Todd Trimble | By the way, it's "ETCS" (Elementary Theory of the Category of Sets), not "ECTS". I went ahead and edited the two places where I spotted the typo. | |
| Jan 22, 2015 at 14:38 | comment | added | Todd Trimble | Most of the classical large categories that arise in a first course, e.g., $Set$, $Grp$, $Top$, etc., can be formalized as having ZFC-style hom-sets to the exact same degree that these categories are presentable as definable classes (i.e., to the degree that there is a ZFC-formula for the notion of "continuous function", say). My reading of an authoritative text such as Mac Lane's -- to the extent that foundational matters are discussed -- is that this point is tacitly understood; the details of such formalization would be out of place. Satisfaction over this point can be left as an exercise. | |
| Jan 22, 2015 at 10:41 | comment | added | arsmath | If you already know about ETCS, then this isn't a question. It's an editorial comment disguised as a question. From the point of view of category theory, any category that is equivalent to the category of sets described by ZFC is obviously sufficient. Whether or not these are pure sets or sets of elephants doesn't matter. If you don't like ZFC, then you can use ETCS plus replacement, as I'm sure you already know. | |
| Jan 22, 2015 at 10:27 | answer | added | Simon Henry | timeline score: 4 | |
| Jan 22, 2015 at 10:25 | history | edited | Peter Smith | CC BY-SA 3.0 |
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| Jan 22, 2015 at 10:11 | comment | added | Peter Smith | Yep, I am indeed interested in ETCS and so forth! My some inchoate query here concerns what is supposed to be going on in the standard intro books when the only set theory the intended reader is likely to know about is good old ZFC! | |
| Jan 22, 2015 at 9:57 | comment | added | Eric Wofsey | It sounds like you may be interested in structural set theory. | |
| Jan 22, 2015 at 9:45 | history | asked | Peter Smith | CC BY-SA 3.0 |