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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
Jan
22
comment SupLat and InfLat
Berci, I know, please look at the comments I wrote to Zhen Lin above
Jan
22
comment SupLat and InfLat
@ZhenLin However what I really found a bit puzzling was the sentence about inclusion functors. It seems (to me) to say that Suplat is included in a different way than InfLat into Pos. But this is obvious, since they are different categories, they are included with different functors. So why write this down? Or does this sentence mean something else subtly different?
Jan
22
comment SupLat and InfLat
It is not a contradiction, but isomorphism is much stronger than equivalence, so why not mention it?
Jan
21
comment SupLat and InfLat
thank you Berci. This is exactly what I thought. I am calling the ncatlab customer service...
Jan
21
accepted SupLat and InfLat
Jan
21
comment What is the “correct” way of making $\mathcal{P}(X)$ into a topological space?
I think your question/construction has to do with Alexandrov topology.
Jan
21
comment Relating categorical properties of arrows
ok! +1 . You can check also for epis and monos in ncatlab
Jan
21
comment Relating categorical properties of arrows
The title as it stands is not really meaningful. I would suggest something along the lines: "Relation between injections and monos".
Jan
21
comment Relating categorical properties of arrows
injection and surjection are not categorical afaik (they use elements of sets). they can be used in concrete categories though. The best/most general table I know is the one mentioned by Marco in his answer and found in the Joy of Cats. These implications are also implemented in the upcoming version of my WildCats package.
Jan
21
asked SupLat and InfLat
Jan
16
revised Demonstrate currying via homomorphism
edited small typos
Jan
16
comment Demonstrate currying via homomorphism
@HenningMakholm I fixed all typos