Tom Leinster
Reputation
Next privilege 20,000 Rep.
Access 'trusted user' tools
 Mar 7 awarded Notable Question Feb 19 awarded Popular Question Feb 1 awarded Good Answer Dec 30 awarded Good Answer Oct 17 awarded Yearling Sep 23 comment The category of elements, enrichment, and weighted limits Just on a terminological point, it seems to me quite eccentric of Wikipedia to use one expression ("Grothendieck construction") for the Cat-valued case and a different expression ("category of elements") for the Set-valued case. After all, the former is a categorification of the latter and the latter is a special case of the former. Personally, I use "category of elements" in all situations; it's a good evocative name. (Plus, Grothendieck came up with many constructions.) To some extent Wikipedia is following tradition, but this particular tradition really doesn't deserve to be perpetuated. Aug 29 comment Classifying spaces for enriched categories Thanks for the clarification. Aug 28 comment Classifying spaces for enriched categories Vidit, I'm not sure what you mean. The 0-simplices of $\Delta C$ are the objects of $C$, sure. But if $x_0$ and $x_1$ are objects of $C$, what is the set of 1-simplices in $\Delta C$ from $x_0$ to $x_1$? And in your item 1, is $f_{ij}$ just any object of $V$? Finally, is this really answered in Bullejos and Cegarra's paper? I could only see the special case $V = \mathbf{Cat}$, i.e. classifying spaces of 2-categories (as their title suggests). Aug 20 comment Categorical product of graphs and chromatic number For all we currently know, there might be an inequality the other way round too (at least, for a finite family of finite graphs). That's exactly Hedetniemi's conjecture. Here's a categorical account: golem.ph.utexas.edu/category/2014/12/… Jun 13 answered Reference for an unbiased definition of a symmetric monoidal category Jun 12 comment A good place where to learn about derived functors Fixed. I've moved jobs since writing this answer, and the link was to my old website. Jun 12 revised A good place where to learn about derived functors updated link Jun 6 comment For a ring $k$ and a set $X$, what are the $k$-algebra homomorphisms $k^X \to k$? Thanks, Eric. So in particular, whether there exist nontrivial maps $k^X \to k$ depends only on $X$ and the cardinality of $k$, at least when $k$ is a field. Jun 6 accepted For a ring $k$ and a set $X$, what are the $k$-algebra homomorphisms $k^X \to k$? Jun 4 comment For a ring $k$ and a set $X$, what are the $k$-algebra homomorphisms $k^X \to k$? @ArturoMagidin: Thanks for the edit, Latexifying the title. I seem to recall a meta discussion a while ago in which various people said Latex in titles should be kept to a minimum. It was a matter of speeding up rendering on slow devices or slow network connections. That's why I wrote the title in plain text. But I'm not so bothered about it that I'm going to change it back. Jun 4 revised For a ring $k$ and a set $X$, what are the $k$-algebra homomorphisms $k^X \to k$? improved wording Jun 4 comment For a ring $k$ and a set $X$, what are the $k$-algebra homomorphisms $k^X \to k$? @TomGoodwillie: Thanks! Your argument implies that if $|X| \leq |k|$ then there are no nontrivial homomorphisms $k^X \to k$, doesn't it? Jun 4 comment For a ring $k$ and a set $X$, what are the $k$-algebra homomorphisms $k^X \to k$? @YCor: I don't have a particular interest in large cardinals, thanks, but neither do I particularly want to rule out sets of large cardinality. Jun 4 asked For a ring $k$ and a set $X$, what are the $k$-algebra homomorphisms $k^X \to k$? May 26 awarded Good Question