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2d
comment Are there examples of families of objects which are canonically isomorphic, but where diagrams of canonical isomorphisms don't commute?
@QiaochuYuan That makes it much clearer; thanks.
2d
comment Are there examples of families of objects which are canonically isomorphic, but where diagrams of canonical isomorphisms don't commute?
@QiaochuYuan I'm not seeing it. For a simple example of what I meant, take a groupoid with one object, say with automorphism group $S_4$. There are five conjugacy classes; what is the group structure on the set of conjugacy classes?
2d
comment Are there examples of families of objects which are canonically isomorphic, but where diagrams of canonical isomorphisms don't commute?
Conjugacy classes of isomorphisms do not form a category in any really sensible way.
2d
answered Obscure Names in Mathematics
Oct
22
comment How did the summation operation come into use?
Matt, I'd like to draw your attention to an Area 51 site which feels to me like a better fit for your question: area51.stackexchange.com/proposals/65204/…
Oct
21
comment Runge-Kutta with all nodes at n+1 or zero weights otherwise
This isn't off-topic, but it has been suggested that the question would attract better answers at scicomp.SE, and so I am migrating...
Oct
21
comment Simple functions on a product measure space
Is this comment addressed to Michael Greinecker?
Oct
20
comment Dirichlet distribution: Normalization of alpha values
It has been suggested that stats.SE is a better venue for this question, and I am inclined to agree. Migrating now...
Oct
19
comment Is every polynomial ring over any field regular?
Wikipedia thinks so: en.wikipedia.org/wiki/Regular_ring (specifically: any field is regular, and if $A$ is a regular ring, so is $A[x]$).
Oct
18
revised Counterexamples in Algebra?
added 99 characters in body
Oct
18
revised Counterexamples in Algebra?
added 99 characters in body
Oct
17
comment Wonderful applications of the Vandermonde determinant
Interesting, but can this be explained to students without much background (as requested in the question)?
Oct
16
revised Extreme unit linear functional not norming a vector
spelling in title
Oct
16
comment Examples of common false beliefs in mathematics
I think the "topologists assume" sentence in the last bullet is unfair; it implies topologists are making mistakes. Certainly competent topologists are not making such rookie mistakes, and are well aware of the standard counterexamples.
Oct
15
awarded  Sheriff
Oct
15
comment Cocomplete but not complete abelian category
I'm not seeing a thing wrong with this, and it's carefully written. Congratulations on this ingenious answer. Just a small note that $k_\beta \otimes_{k_\alpha} -$ preserves arbitrary products iff $k_\beta$ is a finite extension of $k_\alpha$ (being canonically isomorphic to $\hom_{k_\alpha-\text{Vect}}(k_\beta, -)$), in which case the canonical map $k_\beta \otimes_{k_\alpha} W(\alpha) \to W(\beta)$ would be an isomorphism. That's why we needed $k_\beta$ to be an infinite extension of $k_\alpha$.
Oct
15
comment Compactly generated Banach spaces
The phrase "compactly generated" has another meaning in general topology, where continuity of maps out of $X$ can be probed by testing continuity of their restrictions to compact subsets. This would seem to be a condition much different from the one of the OP!
Oct
14
comment Relations In Category Theory
Of course not, @MichalR.Przybylek
Oct
14
comment Relations In Category Theory
All this being said, it's hard to do much with relations in a category $C$ to simulate the usual sort of calculus of relations, unless one assumes more of $C$. For example, to get a half-decent notion of composition of relations, one typically assumes that $C$ is a regular category.
Oct
14
comment What is the minimal $C_k$, such that every $f\colon \{-1,1\}^n\to \mathbb{R}$ of degree at most $k$ satisfies $\|f\|_2\le C_k\|f\|_1$
(I don't detect a link.) If there is a specific result related to Asano contraction that you can give that will answer the question, then please provide it. Otherwise this may have to be moved to a comment, as the question of whether it answers the question is being disputed -- thanks.