12
votes
7answers
2k views

Usage of set theory in undergraduate studies

I would like to ask my colleagues their thought on good practices concerning set theorical framework in undergraduate studies. For example, have there been any attempt to use another mathematical ...
21
votes
11answers
5k views

Categories First Or Categories Last In Basic Algebra?

Recently, I was reminded in Melvyn Nathason's first year graduate algebra course of a debate I've been having both within myself and externally for some time. For better or worse, the course most ...
11
votes
3answers
1k views

Analysis from a categorical perspective

I have not studied category theory in extreme depth, so perhaps this question is a little naive, but I have always wondered if analysis could be taught naturally using categories. I ask this because ...
4
votes
5answers
589 views

Resources for learning domain theory?

I'm a computer programmer who's caught on to denotational semantics. I mostly work with Ruby, JavaScript and C, but I know a little Haskell and ML. I've taken my first steps towards reasoning about ...
15
votes
3answers
810 views

Do rational numbers admit a categorification which respects the following “duality”?

I need to give a lot of quite basic background to this question because I think (at least from conversing with fellow graduate students) that most mathematicians have not really thought about ...
45
votes
9answers
10k views

Relating Category Theory to Programming Language Theory

I'm wondering what the relation of category theory to programming language theory is. I've been reading some books on category theory and topos theory, but if someone happens to know what the ...