2,320 reputation
620
bio website wildcatsformma.wordpress.com
location Somewhere over the rainbow
age
visits member for 2 years, 11 months
seen 3 hours ago

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
9
comment Category objects
@MakotoKato, CliveNewstead , you are both right. Unfortunately the word "set" has different meanings for different people/theories. ZFC uses only sets , but it is too limiting for CT. NGB goes a bit further and uses sets and classes. The Joy of Cats ebook goes even further and uses sets, classes, conglomerates. This corresponds to Grothendieck use of multiple universes U, U',U"... made of U-sets, U'-sets, U"-sets...Makoto Kato uses sets in the sense of Grothendieck ,so they are actually NGB classes.
Jan
5
revised Show that the powerset partial order is a cartesian closed category.
edited title
Jan
5
suggested suggested edit on Show that the powerset partial order is a cartesian closed category.
Dec
29
comment Being a monomorphism described as a universal property
Thank you Zhen Lin, I was aware of these descriptions, but I was hoping to get something along the lines of the general definition of universal arrow (as initial/terminal object in an appropriate slice category, given an appropriate functor).
Dec
29
asked Being a monomorphism described as a universal property
Dec
29
comment Is there a computer program that does diagram chases?
WildCats version 0.60 has been released. It is a major update over the previous release.Cones, Comma categories and Diagonal functors have been introduced.
Dec
27
comment Does fiber product preserve limits?
Indeed it is in Awodey's text, but I was under the impression that this functor F is used in algebraic geometry. So I am asking for an algebraic geometry text, if it is possible. Or, more in general, a good introductory text on algebraic geometry which uses categorical language
Dec
27
comment Does fiber product preserve limits?
Thank you. Could you please suggest an algebraic geometry text where these functors/arguments are used?
Dec
27
comment Does fiber product preserve limits?
The source of my puzzlement is this: $F$ is a functor on a slice cat, whose objects are really morphisms $f$ in $\mathcal{C}$. So - by writing the functor $F$ in that way - you end up with expressions like $f \times_S S'$ where you have a fiber product between a morphism $f$ and an object $S'$. I wonder : is this standard notation? if yes, where?
Dec
27
comment Does fiber product preserve limits?
I understand how you and Makoto Kato are definng F, but I have a question: is your notation really correct? The way you write it $(-) \times_S S'$ appears to be a functor in $\mathcal{C}$ and not on the slice, and can be misleading, as shown below in Augusti Roig question/comment
Dec
14
revised Universal arrows' definition
edited text
Dec
13
revised Universal arrows' definition
edited small typos
Dec
13
comment Universal arrows' definition
The above diagrams were composed with my package WildCats wildcatsformma.wordpress.com . It is a freely available category theory package for Mathematica.
Dec
13
answered Universal arrows' definition
Dec
11
revised How to characterize categories which their only isomorphisms are identities?
edited title
Dec
11
suggested suggested edit on How to characterize categories which their only isomorphisms are identities?
Dec
11
comment Universal arrows' definition
Welcome Esther to math stackexchange! I am on the road so, if you can wait about 24 hours, I will post a precise answer to your question
Dec
8
comment Why isn't the covariant powerset functor representable?
Why do you write: "$\mc C(A,-)$ is contravariant" ?
Dec
7
comment The importance of parallel arrows in a commutative square
The above diagrams were composed with my package WildCats wildcatsformma.wordpress.com . It is a freely available category theory package for Mathematica from Wolfram Research
Dec
7
revised The importance of parallel arrows in a commutative square
added last paragraph