slideshow 3

Complexity seminar

Who needs category theory?

Yuri Gurevich
University of Michigan

 

Friday, 13. September 2019 - 13:30 to 15:00

in IM, rear building, ground floor

Mathematicians use category theory, at least some of them do. In fact category theory
is instrumental in some branches of mathematics, e.g. algebraic topology. But what
about computer scientists or physicists? Do they need category theory?

If category theory is your hammer, some computing problems look like appropriate
nails. However the speaker was not impressed and remained skeptical about the use of
category theory in computer science. When he learned that the generally accepted
mathematical basis for topological quantum computing is sophisticated category theory,
he proposed to his long-time collaborator Andreas Blass to "decategorize" topological
quantum computing.

It turned out, surprisingly, that category theory or something like it is necessary
for topological quantum computing. Moreover the root cause of the necessity is not
specific to topological quantum computing. There should be numerous other computing
problems where something like category theory is necessary. Understanding the root
cause allowed us to simplify the mathematical basis for the topological quantum
computing and to decategorize it to the extent possible.

In the main part of the talk, without assuming any knowledge of category theory or
quantum computing, we illustrate, on a simplified example, why category theory or
something like it is necessary for topological quantum computing.