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bio website wildcatsformma.wordpress.com
location Somewhere over the rainbow
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visits member for 3 years, 2 months
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My scientific interests:

  • Mathematics: Category Theory, Algebra, Logic (Model-Theory, ATP), Control Systems
  • Physics: General Relativity, QFT
  • Amateur Astronomer and Astrophotographer
  • Mathematica programming

My Website:WildCats
Premiere Mathematica package for category theory

Visit the newly launched Mathematica.SE!

My non-scientific interests:

  • Skiing, Sailing, Windsurfing
  • Argentine Tango dancer

More or less fluent in (random order):

Italian, English, German, French, Spanish, Dutch and struggling with Russian


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
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
16
comment Demonstrate currying via homomorphism
@HenningMakholm I fixed all typos
Dec
24
comment A Tool to practice Categories / Allegories
@qartal yes, you have to type $BaseDirectory, or $UserBaseDirectory in Mathematica and see what folder location it gives back to you. Then place the package in that folder. These are standard operations for Mathematica users. Search the help file for $BaseDirectory to get more info.
Dec
20
comment A Tool to practice Categories / Allegories
I also do not understand. Please see my answer below.
Nov
21
comment Why is this not a category?
Indeed the claim is false. Does this category of monotone functions have a standard name?
Nov
21
comment Why is this not a category?
your first formula has typos, you may wish to correct it
Nov
15
comment On conglomerates' axiom of choice(Category theory)
User45765 What book/text are you referring to? The "Joy of cats" perhaps?
Nov
11
comment Connection between categorical notion of adjunction and dual space/adjoint in vector spaces
Can you please quote some economics textbook using these mathematics? The introductory textbooks I am aware of , barely use calculus.
Nov
5
comment Identifyng objects in a category
I never said the question was "stupid" or anything (I even upvoted it).I never said the question did not make sense at all. My advise was of a more general nature - a tactics you might say: whenever you want to invent/reinvent/discover/rediscover something in category theory, think at morphisms first, then objects will fall in line automatically. Granted,we intuitively all think in terms of objects, but the challenge (and the reward) in category theory is to think in terms of morphisms. Is this not true?
Oct
31
comment Functor between two categories
thank you.This result does not seem to be readily available everywhere, otherwise you would not need to ask us here. Is your course/homework online, so that I can see it ?
Oct
31
comment Functor between two categories
Was this question inspired by some book/text? Could you please post a reference?
Oct
30
comment Derive the unit from the adjunction
CWM 2nd ed. page 80 gives a clear derivation of the naturality of $\theta$ (he calls it $\phi$) both in $C$ and in $D$. This is a more general result than the one you wish to obtain. I also edited a couple of things.