Uday Reddy
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 Feb18 comment Definition of (projective ?) limit in a presheaf category. "Projective limit" is their terminology for what is normally called a "limit". Their "inductive limit" is what is normally called a "colimit". Dec7 comment Good books and lecture notes about category theory. Eilenberg and Mac Lane's original paper: General theory of natural equivalences says that they defined "category" to define "functor", and "functor" to define "natural transformation". But I get the impression that the category theorists of today don't take that remark all that seriously. Nov30 comment When should we take direct limit and when should we take inverse limit? I think a correction is warranted: The direct limit is not a subset of the union. It is a quotient of the disjoint union. 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". 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 :-) 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 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. 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? 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. Aug25 comment Equality of two notions of tensor products over a commutative ring It is not clear what you are saying. There are two classes of maps being talked about, and each of them has a "universal element" in your terminology. They have no reason to be isomorphic just by virtue of being "universal" (in their own class). Aug24 comment Mathematical notation for computer science There is no single piece of notation that is used in Computer Science, and it is also unlikely that you will find it all in one place. Depending on the subject area you are looking at, you would need to find perhaps a graduate text book on the subject to get all the background you need. Apr17 comment Why bifunctors? @ZhenLin. Yes, I see that now. However, note that nobody thought of calling natural transformations "binatural transformations". Occam's razor should win eventually. Apr17 comment Why bifunctors? Ok, I guess that is a reasonable explanation. I was under the mistaken assumption that the morphism-bimorphism distinction is only made when there is a product and a separate tensor product, because there would then be a real need to distinguish between the two concepts. You are saying that the "bimorphism" terminology can be used whenever there is a closed symmetric monoidal structure. Apr17 comment Why bifunctors? @dtldarek. Yes, that analogy would make sense. In the same way that the tensor product may be seen as an "artificial" construction to make bilinear transformations look linear, one might regard dual category as an artificial construction to make mixed variant functors look functorial. However, the "bifunctor" term is used even when there is no mixed variance. Apr17 comment Why bifunctors? But my understanding is that bilinear maps are not linear maps or vice versa. So, there you do need different terms.