Talk:S-construction
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No need for a separate article
[edit]I think this article should be moved to a section of Waldhausen category. S-construction may only be applied to Waldhausen categories, and also the opposite is true: I suspect there isn't even a single research paper which uses Waldhausen categories but doesn't apply S-construction to them. Dpirozhkov (talk) 01:17, 6 December 2017 (UTC)
- Well, shouldn't the construction be more general than Waldhausen category? i.e., the construction can potentially be generalized, say to some higher category. If so, perhaps the better idea is to merge Waldhausen category into this article. -- Taku (talk) 03:40, 6 December 2017 (UTC)
- That's technically true, but it goes against my intuition of what's primary and what's secondary. S-construction may be generalized, but it may also have slight modifications which calculate the same thing. So, morally, the particular construction shouldn't be a defining feature, even though that's the only definition we have. A more serious argument is that when people discuss K-theory of other kinds of categories, e.g. dg-categories or infinity-categories, they say "here's how to produce a related Waldhausen category, take K-theory of it" and don't mention the explicit construction (for example [1] or [2]). So for them, Waldhausen categories are primary objects. Anyway, it's probably easier to just leave two articles separate for now, I don't mind any result. Dpirozhkov (talk) 05:49, 6 December 2017 (UTC)
- Having said the above, I don't have a strong opinion; also the merger would result in the better readers experience (forgive me for a dread expression). So, I simply merged it into the Waldhausen category article. -- Taku (talk) 23:05, 24 June 2018 (UTC)
- That's technically true, but it goes against my intuition of what's primary and what's secondary. S-construction may be generalized, but it may also have slight modifications which calculate the same thing. So, morally, the particular construction shouldn't be a defining feature, even though that's the only definition we have. A more serious argument is that when people discuss K-theory of other kinds of categories, e.g. dg-categories or infinity-categories, they say "here's how to produce a related Waldhausen category, take K-theory of it" and don't mention the explicit construction (for example [1] or [2]). So for them, Waldhausen categories are primary objects. Anyway, it's probably easier to just leave two articles separate for now, I don't mind any result. Dpirozhkov (talk) 05:49, 6 December 2017 (UTC)