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 Mar11 revised Cartesian Product characterization in Rel Category (Category of sets and relations) in simpler terms edited title Mar10 comment Cartesian Product characterization in Rel Category (Category of sets and relations) in simpler terms ....This description is made using concepts from monoidal categories,so I think that you need to study them a bit if you want to understand this part of the answer given by Zhen Lin. Mar10 comment Cartesian Product characterization in Rel Category (Category of sets and relations) in simpler terms Qartal the Q&A you mentioned has 2 parts.The first part proves that the categorical product of 2 objects $Y$, $Z$ (which are sets) in the category $Rel$ is given by the object (which is a set) that you would call "the disjoint union of $Y$ and $Z$".This part has nothing to do with the cartesian product of $Y$ and $Z$.The second part describes/characterizes the object of $Rel$ that you would call "the cartesian product of $X$ and $Y$"... Mar7 comment What's the explicit categorical relation between a linear transformation and its matrix representation? By the way Henning, is there a way to construct categorically $FVectB_F$ from $FVect_F$ (and some other category), in the same spirit that the category of pointed sets $Set_*$ is built from $Set$ : as a comma category Mar7 comment Matrix associated to a linear transformation Yes Aluffi is the best probably. Lang's Algebra unfortunately does not emphasize the categorical viewpoint Mar7 comment Projection morphisms of categorical product In the penultimate paragraph, "...for an automorphism $u$" should be "...for an isomorphism $u$", I think Feb8 comment Lost Chevalley Manuscript I also read that end note and always found very very strange that Chevalley never bothered to rewrite the manuscript or keep a copy for himself. Feb7 answered Category with no empty hom-sets from a given category. Feb6 comment Corverting topological problems to algebraic problems @drhab I do not understand: if Laters is the downvoter for the 2 answers, why I do not see a loss of 2 points in his reputation? Feb6 comment Category with no empty hom-sets from a given category. a category with no empty homs may - in general - be very different from a preorder. A preorder may have empty homs. So , like @tcamps I suggest you clarify your question Jan28 comment Question about general comma categories I suggest you to use the Wikipedia Definition of category which does not talk about hom disjointness, but it derives it as a consequence. Jan28 comment Question about general comma categories Jim's a,b,c Z construction is - very strictly speaking - not a category because the dom and cod functions are undefined. But of course anybody with a minimum of mathematical experience (or simple common sense) can figure out that all you need to upgrade the structure to the category status is just to write $$and$$ to distinguish different morphisms which were initially just called $n$. Cont.d Jan28 comment Question about general comma categories @CC0607 the disjointness condition is VERY important, but it is enforced stating that a category comes with cod and dom functions associating to each morphism a domain and a codomain. Najib points you to a relevant q&A but then - inexplicably to me - comes to the opposite conclusion. Remember his reference, forget his comment. Cont.d Jan27 comment Where can I find linear algebra described in a pointfree manner? I am... speechless Jan27 comment Where can I find linear algebra described in a pointfree manner? interesting question, however... if it's pointfree, what's the point studying it? :-) Jan26 comment Question about general comma categories you are welcome and if you found my other answer valuable you kindly are invited to upvote it. Jan26 comment Question about general comma categories continued from above. Comma cats are one such case: you already have named morphisms in the base categories, so you need a precise notation to allow you to recover the domain and codomain information. That's why you need a quadruple. Jan26 comment Question about general comma categories Look, the basic rule is: different things should be written in different ways, so you can see that they are different (and you can make calculations, manually or automatically with a PC). You can of course write morphisms as triples, but that is overkill in 99% of the cases. You would than need a quadruple of triples to describe a morphism in a comma category. So you do that only in special cases as in @Jim example with Z, where you cannot freely choose the names of the morphisms. continued below Jan26 answered Question about general comma categories Jan22 comment SupLat and InfLat Yes, the "non obvious inclusion" is quite obvious to me. You can always compose a functor with an isomorphism (or some other functor) and get a new functor. I would not call this new functor an inclusion though, since it does not send an object to itself (CWM page 15). It is interesting to note that inclusion functor is an empty page in ncatlab. Anyway, thank you Zhen Lin, it does not seem that I missed anything subtle on this ncatlab page