Questions and answers -- a category arising in linear logic, complexity theory, and set theory

TL;DR

This paper explores a category that appears in linear logic, set theory, and complexity theory, revealing its structure and proposing new connectives inspired by its applications across these fields.

Contribution

It describes a unifying category across multiple disciplines and introduces new multiplicative connectives for linear logic based on these insights.

Findings

The category appears in linear logic, set theory, and complexity theory.

It suggests new multiplicative connectives for linear logic.

The set-theoretic application indicates a sequential composition connective.

Abstract

A category used by de Paiva to model linear logic also occurs in Vojtas's analysis of cardinal characteristics of the continuum. Its morphisms have been used in describing reductions between search problems in complexity theory. We describe this category and how it arises in these various contexts. We also show how these contexts suggest certain new multiplicative connectives for linear logic. Perhaps the most interesting of these is a sequential composition suggested by the set-theoretic application.