Categorical Comprehensions and Recursion

TL;DR

This paper introduces a new categorical framework to characterize subrecursive classes within complexity hierarchies using coercion functors and recursion schemes that mimic bounded recursion.

Contribution

It develops a categorical setting that captures subrecursive classes through coercion functors and recursion schemes, providing a categorical counterpart to safe recursion and composition.

Findings

Categorical framework characterizes subrecursive classes

Recursion schemes imitate bounded recursion

Provides a categorical counterpart to safe recursion

Abstract

A new categorical setting is defined in order to characterize the subrecursive classes belonging to complexity hierarchies. This is achieved by means of coercion functors over a symmetric monoidal category endowed with certain recursion schemes that imitate the bounded recursion scheme. This gives a categorical counterpart of generalized safe composition and safe recursion.