2024-04-05: Jade Master (MSP)

Tue, 2 Apr 2024 16:49:45 +0000

Jade Master (MSP)

I Think Indexed Enriched Categories are Nice.

Abstract

First proposed by Lawvere in 1973, indexed enriched categories are a very complicated mathematical structure studied in only the most privileged ivory towers. In this talk I intend to bring them down to earth by exploring their viability as a data structure. I will cheat by only considering enrichments where the axioms are satisfied trivially. I will explain how these 'trivial' enriched categories are nice data structures for holding solutions to algebraic path problems. Then I will explain how making them indexed allows us to work with distributed, concurrent, and compositional algebraic path problems. This talk will be in line with the research programme I started to develop before I quit and left for industry. Namely, that indexed categories and Grothendieck constructions may be used to develop a general theory of compositional computation. This talk will feature Idris2 code and categorical terminology side-by-side so that those familiar with either language will be able to follow along.

2024-04-05 15:00:00 UTC
LT209 and Online