Category Theory For Computer Science

Prof. Michael A. Gennert
WPI Computer Science Department

Friday, September 8, 1995
11 a.m. - 12 noon
Fuller Labs 311

Category Theory is a branch of abstract mathematics that has many connections with Computer Science. The connections can be felt in the design of programming languages, semantic models, type theory and polymorphism, constructive logic, automata, concurrency, software engineering, and user interfaces.

A category is simply defined. It consists of:

We write f : A -> B to indicate that f is an arrow with domain A and codomain B. There are a few restrictions:

And that's all. Most common set-theoretic concepts, such as product, union, injection, and surjection, have category-theoretic analogues. This is not surprising; there is a category called SET whose objects are sets and whose arrows are total functions. Other commonly encountered categories are sets and partial functions, partial orders and monotone functions, monoids and monoid homomorphisms, groups and group homomorphisms, and graphs and graph homomorphisms. Things start getting complicated, and interesting, when we treat categories as objects and maps among them as arrows.

This talk will touch on these ideas, with examples drawn from Computer Science. It will be accessible to anyone with a good understanding of Discrete Mathematics.

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Last modified: Sep 27, 2006, 16:05 EDT