Timeline for Lax universality for lax limits
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 12, 2010 at 15:47 | vote | accept | Alan Jeffrey | ||
| Nov 2, 2010 at 14:31 | comment | added | Alan Jeffrey | The category theory mailing list may be the way to go. Dusko can be annoyed with me for asking the $n+1$th terminological question :-) "Lax products" aren't determined up to iso, but (quick scribbles on back of envelope) up to a "lax iso", that is for any candidates $Z$ and $Z'$ there are morphisms $f : Z \rightarrow Z'$ and $f' : Z' \rightarrow Z$ such that $1 \Rightarrow f;f'$ and $1 \Rightarrow f';f$. | |
| Nov 2, 2010 at 5:13 | comment | added | Mike Shulman | BTW, is such a "lax product" uniquely characterized up to iso by its universal property? Offhand I don't see why it would be... and if not, I'd be a little uneasy about calling it any kind of "limit" rather than regarding it instead as some kind of algebraic structure on the category. | |
| Nov 2, 2010 at 5:11 | comment | added | Mike Shulman | This might be a good question for the categories mailing list. It seems like there might be a chance of its being in the literature somewhere, but if so, the people who would know may not be reading MO. | |
| Nov 2, 2010 at 1:30 | comment | added | Alan Jeffrey | That is indeed what I'm after. The particular case is smash product, but there's obvious generalization to an arbitrary (weighted) limit. Partly my concern is just terminological: I have a paper to write and I need a name for the gadget I have! But I'd also like to make sure it generalizes properly. | |
| Nov 1, 2010 at 20:57 | answer | added | Finn Lawler | timeline score: 2 | |
| Nov 1, 2010 at 20:33 | comment | added | Mike Shulman | In other words, you want an object $P$ with projections $p\colon P\to A$ and $q\colon P\to B$ such that the induced functor $Hom(X,Y) \to Hom(X,A)\times Hom(X,B)$ has an adjoint? I haven't seen this specifically in the literature, but you may be interested in the related notion(s) of lax 2-adjunction: ncatlab.org/nlab/show/lax+2-adjunction | |
| Nov 1, 2010 at 17:21 | history | asked | Alan Jeffrey | CC BY-SA 2.5 |