Does anyone know how "appendices" to papers work, when they're written by another person? Do both people (the writer of the main body and the writer of the appendix) get authorial credits in citations?
@JonathanBeardsley Google Scholar sometimes pretends you're the author, sometimes it completely ignores it. Again, n=1 for Michel. His appendix to a paper of Keller is listed as a publication, the other 3 appendices are not.
4 hours later…
user131753
1:56 PM
Let $\mathbf{A}$ be a category and $\mathbf{A}^{\text{op}}$ be the dual category of $\mathbf{A}$. Let $A,B$ be any two $\mathbf{A}$-object. In this book it is written that $\operatorname{Hom}_{\mathbf{A}^{\text{op}}}(A,B)=\operatorname{Hom}_{\mathbf{A}}(B,A)$.
user131753
In particular if we consider $\mathbf{A}=\mathbf{Set}$ then how can the same $f$ belong to the both $\text{Hom}$-sets? Isn't a function $f\in \operatorname{Hom}_{\mathbf{A}}(A,B)$ a subset of $A\times B$ and $f\in \operatorname{Hom}_{\mathbf{A}^{\text{op}}}(B,A)$ a subset of $B\times A$?
user131753
That being said, is there any way to identify dual categories of a category in $\text{CAT}$ (via, say some universal property)?
@user170039 Uhm I don't know a good reference (in fact I know only of a reference for the same fact for â-cats), although it must be a super classical fact. The idea is to see what the automorphism is doing to posets of the form [n]={0<...<n}. Also, when I say "automorphism" I really mean automorphism of the (2,1)-category Cat, not of the 1-category. I don't know if it is true for the 1-category (it's probably true, but I'm not going to commit)
That is to say, the automorphism must induce equivalences on the groupoids of functor and natural isomorphisms, not bijection on the set of functors
what is the precise relationship between the Drinfel'd-Katz-Mazur moduli problem [Gamma_0(p)] and TMF^0(BSigma_p)/transfer?
i don't expect them to be the same, but if power operations on TMF are indeed to be dictated by subgroups of order p, i'd expect them to be almost the same
might be easier to answer this at (p=2, say) for the simultaneous moduli problem (M_1(3), [Gamma_0(2)] ) and TMF_1(3)^0(BZ/2)/transfer
