2,373 reputation
1720
bio website wildcatsformma.wordpress.com
location Somewhere over the rainbow
age
visits member for 3 years, 1 month
seen Dec 15 at 15:38

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 In the morphisms-are-functions view of category theory, how are poset categories explained?
"Some people have taken the view that morphisms in category theory ought to simply be called functions". Some people? what people? Oh please!
Jan
21
comment Properties of Group $\to$ Monoid $\to$ Semigroup.
there is some strange problem with this page: I am trying to upvote the question, but I cannot do it. Looks like the title interferes with the up-arrow. Also the link to Arturo's answer does not work properly even if it is pointing correctly. Anybody else has this problem?
Jan
21
revised Fixed points in category theory
Changed mapsto to to
Jan
21
suggested approved edit on Fixed points in category theory
Jan
17
comment Categories of $n$-ary relations?
@alancalvitti I have read them, but still I do not see why you think or worry that Rel might not be enough. Could you perhaps describe a relation you have in mind and we can see if it fits into Rel?
Jan
16
comment Categories of $n$-ary relations?
@alancalvitti I do not really understand either. Could you please make a concrete example of these relations?
Jan
13
comment Properties of $\mathbf{Cat}$
@MakotoKato got it, thanks
Jan
13
comment What is the free category on the underlying graph of a category?
@ZhenLin Actually, if I understand correctly, the question is: is $Free(U(\mathcal{D}))$ different from $\mathcal{D}$, where $\mathcal{D}$ is a category and U is the forgetful functor $U:Cat \to Graph$
Jan
13
comment Properties of $\mathbf{Cat}$
Dear @MakotoKato I am not able to access the BBP article. If you consider that it has the correct definition of congruence, I would be very interested to see it. You could post it as an answer to your own question (this is a perfectly accepted practice) and I would be more than happy to upvote your answer.
Jan
11
answered Properties of $\mathbf{Cat}$
Jan
11
comment Properties of $\mathbf{Cat}$
@MakotoKato you may find Awodey easier to follow. Please check: andrew.cmu.edu/course/80-413-713/notes chapter 4, pages 73-78. Especially exercises 6-8 at the end too. If the exercises are too much for you, Awodey kindly provides answers here: andrew.cmu.edu/course/80-413-713/hw/sol.pdf . Enjoy the weekend
Jan
9
comment Properties of $\mathbf{Cat}$
@MakotoKato Ittay Weiss indicated how you can find coequalizers in Cat in a comment above:If $F,G:C \to D$ are functors then a coequalizer is the quotient of D by the congruence generated by equating F(x) with G(x). This is very similar to what happens in Set. If you think that functors are essentially functions of morphisms and that categories are essentially collections of morphisms, your intuition should help you fill the gory details of the proof.
Jan
9
comment Definition of a diagram in a category
@MakotoKato CWM 2nd ed. page 71 gives an alternative definition:diagram in C of shape G is a morphism $D : G\to UC$ of graphs.
Jan
9
revised Product in a preorder
edited supremum -> infimum
Jan
9
comment Product in a preorder
@JohnMyers I edited the question, so now it looks correct
Jan
9
suggested approved edit on Product in a preorder
Jan
9
comment Properties of $\mathbf{Cat}$
@MakotoKato CWM 2nd edition, page 112 exercise 5 asks you to prove that Cat is small-complete. It gives you all the tools you need in the preceding pages. You may prefer The Joy of Cats page 211 and following to get extra/different insights
Jan
9
comment Definition of a diagram in a category
@MakotoKato Wikipedia says:"The actual objects and morphisms in J are largely irrelevant, only the way in which they are interrelated matters". This simply means that the actual names of objects and morphisms are irrelevant (of course), but the interrelations matter. This is a common theme in CT. I think you confuse the "diagram" which is a functor with its image in the codomain category. It is true that the image counts more, but we still need the functor so that we can compose functors (and -in a sense- transfer the diagrams) and find if and how limits are preserved or created.
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