Reputation
2,565
Top tag
Next privilege 3,000 Rep.
Cast close and reopen votes
Badges
1 7 21
Impact
~22k people reached

Mar
11
revised Cartesian Product characterization in Rel Category (Category of sets and relations) in simpler terms
edited title
Mar
10
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.
Mar
10
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 $Y$"...
Mar
7
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
Mar
7
comment Matrix associated to a linear transformation
Yes Aluffi is the best probably. Lang's Algebra unfortunately does not emphasize the categorical viewpoint
Mar
7
comment Projection morphisms of categorical product
In the penultimate paragraph, "...for an automorphism $u$" should be "...for an isomorphism $u$", I think
Feb
8
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.
Feb
7
answered Category with no empty hom-sets from a given category.
Feb
6
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?
Feb
6
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
Jan
28
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.
Jan
28
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 $<a,n,b>$ and $<b,n,c>$ to distinguish different morphisms which were initially just called $n$. Cont.d
Jan
28
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
Jan
27
comment Where can I find linear algebra described in a pointfree manner?
I am... speechless
Jan
27
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? :-)
Jan
26
comment Question about general comma categories
you are welcome and if you found my other answer valuable you kindly are invited to upvote it.
Jan
26
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.
Jan
26
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
Jan
26
answered Question about general comma categories
Jan
22
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