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I am curious how many people know about the Category Theory? I asked one of the Math professors and he had no idea, though we was teaching Group Theory at the

I am curious how many people know about the Category Theory? I asked one of the Math professors and he had no idea, though we was teaching Group Theory at the time.

zitterbewegung 15y ago
Which college? Note that category theory is heavily used in topology but homological algebra is used in abstract algebra (group theory). See http://en.wikipedia.org/wiki/Category_theory http://en.wikipedia.org/wiki/Category_theory
- DanielRibeiro 15y ago
  It is also used in eliptic and hyperelliptic curve cryptography, when you study the Jacobian Variety a curve: http://modular.math.washington.edu/edu/Fall2003/252/lectures/10-15-03/10-15-03-lecture.pdf http://modular.math.washington.edu/edu/Fall2003/252/lectures... Categories and Functors come out naturally when studying such structures.
- eldina 15y ago
  I think category theory is rarely essentially used in a first or second typical course on some topic in math. Once in a while if students can be assumed to have had a course in category theory, then it is more elegant and efficient e.g. simply to show that some functor has an adjoint hence this or that limit is preserved, but to me category theory, except if it is the main topic of interest, is useful because it eases communication and allows you to quickly get some understanding of a construction that might look very "local" to some category that you are not familiar with. Unlike the person who created the cited notes, I think it actually can help understanding the things under study or the associated constructions, assuming sufficient command of category theory. I remember when I first understood the definitions of things like products, coproducts, push-outs and pull- backs etc. in my last year as an undergraduate. Suddenly, for many of the constructions from topology and algebra it became easier to remember them, how they were constructed and which properties they had. To me it is kind of like with design patterns, mainly I don't use them as tools picked up from my tool box when solving a problem, rather they simply allow me to communicate more easily and gives me another level of abstraction where I can reuse thinking I have done earlier.
eldina 15y ago
Not being a native speaker, I have to ask: Is a "professor" not someone who at least majored in math ?
- groovy2shoes 15y ago
  A professor is a "high-ranking" teacher at a university. You can have a professor in pretty much any field, so there are math professors.
  - eldina 15y ago
    Ok. Then I think it is a little sad that a math professor can now nothing about category theory.
    - xyzzyz 15y ago
      Why? Would you say the same thing about, say, ergodic theory, languages, automata and computation theory, analytic number theory, harmonic analysis, bordism and cobordism, algebraic K-theory, de Rham cohomology, Diophantine approximation, model theory and theory of forcing, descriptive set theory, algebraic geometry, representation theory... I could go on like this forever. People tend not to know that most of the stuff a math graduate learned was already known by 30s, and category theory was only starting to become anything close to popular in 50s - 60s. People also tend not to know just how much math research have been done, especially in last 70 years.
gtani 15y ago
slide 2 And Category Theory is not even taught here.

I am curious how many people know about the Category Theory? I asked one of the Math professors and he had no idea, though we was teaching Group Theory at the time.

zitterbewegung 15y ago

Which college? Note that category theory is heavily used in topology but homological algebra is used in abstract algebra (group theory). See http://en.wikipedia.org/wiki/Category_theory http://en.wikipedia.org/wiki/Category_theory

DanielRibeiro 15y ago
It is also used in eliptic and hyperelliptic curve cryptography, when you study the Jacobian Variety a curve: http://modular.math.washington.edu/edu/Fall2003/252/lectures/10-15-03/10-15-03-lecture.pdf http://modular.math.washington.edu/edu/Fall2003/252/lectures... Categories and Functors come out naturally when studying such structures.
eldina 15y ago
I think category theory is rarely essentially used in a first or second typical course on some topic in math. Once in a while if students can be assumed to have had a course in category theory, then it is more elegant and efficient e.g. simply to show that some functor has an adjoint hence this or that limit is preserved, but to me category theory, except if it is the main topic of interest, is useful because it eases communication and allows you to quickly get some understanding of a construction that might look very "local" to some category that you are not familiar with. Unlike the person who created the cited notes, I think it actually can help understanding the things under study or the associated constructions, assuming sufficient command of category theory. I remember when I first understood the definitions of things like products, coproducts, push-outs and pull- backs etc. in my last year as an undergraduate. Suddenly, for many of the constructions from topology and algebra it became easier to remember them, how they were constructed and which properties they had. To me it is kind of like with design patterns, mainly I don't use them as tools picked up from my tool box when solving a problem, rather they simply allow me to communicate more easily and gives me another level of abstraction where I can reuse thinking I have done earlier.

eldina 15y ago

Not being a native speaker, I have to ask: Is a "professor" not someone who at least majored in math ?

groovy2shoes 15y ago
A professor is a "high-ranking" teacher at a university. You can have a professor in pretty much any field, so there are math professors.
- eldina 15y ago
  Ok. Then I think it is a little sad that a math professor can now nothing about category theory.
  - xyzzyz 15y ago
    Why? Would you say the same thing about, say, ergodic theory, languages, automata and computation theory, analytic number theory, harmonic analysis, bordism and cobordism, algebraic K-theory, de Rham cohomology, Diophantine approximation, model theory and theory of forcing, descriptive set theory, algebraic geometry, representation theory... I could go on like this forever. People tend not to know that most of the stuff a math graduate learned was already known by 30s, and category theory was only starting to become anything close to popular in 50s - 60s. People also tend not to know just how much math research have been done, especially in last 70 years.

gtani 15y ago

slide 2 And Category Theory is not even taught here.