Uday Reddy
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 May8 comment How to get a group from a semigroup It seems to be that, in the Added note, all occurrences of "right adjoint" should be changed to "left adjoint". Apr7 awarded Yearling Apr6 comment Why is the tensor product important when we already have direct and semidirect products? Ok, that is nice! Do you have a reference that discusses this? Apr5 comment Why is the tensor product important when we already have direct and semidirect products? 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. Apr4 comment Why is the tensor product important when we already have direct and semidirect products? What happens if $R$ is not commutative? Apr1 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 :-) Apr1 accepted Homsets of group actions related to fixed points Mar31 asked Homsets of group actions related to fixed points Mar29 revised Analogy for Cosets, Ideals, and Quotient Rings Added a footnote on normal subgroups Mar28 answered Analogy for Cosets, Ideals, and Quotient Rings Feb7 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 $A$. Feb7 awarded Commentator Feb7 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. Feb6 answered Categorial definition of subsets Feb4 answered The importance of parallel arrows in a commutative square Feb2 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? Jan23 answered In the morphisms-are-functions view of category theory, how are poset categories explained? Sep3 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. Aug31 awarded Citizen Patrol Aug26 revised Universal property of tensor product Minor corrections