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.

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.