Who Needs Category Theory?

11 pages•Published: March 7, 2020

Abstract

In mathematical applications, category theory remains a contentious issue, with enthusiastic fans and a skeptical
majority. In a muted form this split applies to the authors of
this note. When we learned that the only mathematically sound
foundation of topological quantum computing in the literature is
based on category theory, the skeptical author suggested to "decategorize" the foundation. But we discovered, to our surprise, that
category theory (or something like it) is necessary for the purpose,
for computational reasons. The goal of this note is to give a high-
level explanation of that necessity, which avoids details and which
suggests that the case of topological quantum computing is far
from unique.

Keyphrases: category theory, computational logic, mathematical logic, topology, witness manipulation

In: Laura Kovacs, Konstantin Korovin and Giles Reger (editors). ANDREI-60. Automated New-era Deductive Reasoning Event in Iberia, vol 68, pages 26-36.

Links:	https://easychair.org/publications/paper/gvcD
	https://doi.org/10.29007/4dr3