451 reputation
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bio website cs.bham.ac.uk/~udr
location Birmingham
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visits member for 2 years, 4 months
seen Jul 18 at 20:41

Professor of Computer Science, with research interests in Programming Languages and Theory of Programming.

My profiles on Theoretical Computer Science, Computer Science, Mathematics, Stackoverflow, and Superuser.

Also on Programmers, where I am shooting for a negative rating (if such a thing is possible)!


Apr
7
awarded  Yearling
Apr
6
comment Motivation for Tensor Product
Ok, that is nice! Do you have a reference that discusses this?
Apr
5
comment Motivation for Tensor Product
I don't think so. The collection $Hom_R(X,Y)$ of $R$-modules for a non-commutative ring $R$ does not have the structure of an $R$-module. See the paragraph 7.5 of my Notes on Semigroups for example.
Apr
4
comment Motivation for Tensor Product
What happens if $R$ is not commutative?
Apr
1
comment Homsets of group actions related to fixed points
Fantastic! Thanks very much. I was probably too exhausted to understand it last night. But, I had chat with an 'expert' this morning, who made it all clear to me :-)
Apr
1
accepted Homsets of group actions related to fixed points
Mar
31
asked Homsets of group actions related to fixed points
Mar
29
revised Analogy for Cosets, Ideals, and Quotient Rings
Added a footnote on normal subgroups
Mar
28
answered Analogy for Cosets, Ideals, and Quotient Rings
Feb
7
comment Categorial definition of subsets
I think what you might need is a 10-minute exercise: Prove that, in category Set, the subobjects of $A$ (as clarified above) are one-to-one with the subsets of $A$.
Feb
7
awarded  Commentator
Feb
7
comment Categorial definition of subsets
You cannot make a statement like $\{1,2\} \subseteq \{0,1,2\}$ categorically, let alone distinguish it from another. What you might say is that $\langle \{1,2\}, u\rangle$ is a subject of $\{0,1,2\}$ where $u$ is the injection of $\{1,2\}$ in $\{0,1,2\}$. But then neither $\langle \{0,1\},u \rangle$ nor $\langle\{1,5\},u\rangle$ is a subobject because $u$ doesn't type-check in those cases.
Feb
6
answered Categorial definition of subsets
Feb
4
answered The importance of parallel arrows in a commutative square
Feb
2
comment Unit of adjunction: Epimorphism?
I can hardly think of any cases where the unit of an adjunction is an epimorphism. Perhaps you meant to ask whether the counit of an adjunction is an epimorphism?
Jan
23
answered In the morphisms-are-functions view of category theory, how are poset categories explained?
Sep
3
comment Universal property of tensor product
@MTurgeon, This question is not a duplicate of math.stackexchange.com/questions/184627/…. That question asked about the "other direction" (proving the first property from the second). On the other hand, the concern is here is how to produce the second (universal $A$-bilinear map) from the first.
Aug
31
awarded  Citizen Patrol
Aug
26
revised Universal property of tensor product
Minor corrections
Aug
26
answered Universal property of tensor product