Picture of virus under microscope

Research under the microscope...

The Strathprints institutional repository is a digital archive of University of Strathclyde research outputs.

Strathprints serves world leading Open Access research by the University of Strathclyde, including research by the Strathclyde Institute of Pharmacy and Biomedical Sciences (SIPBS), where research centres such as the Industrial Biotechnology Innovation Centre (IBioIC), the Cancer Research UK Formulation Unit, SeaBioTech and the Centre for Biophotonics are based.

Explore SIPBS research

What is a categorical model of arrows?

Atkey, Robert (2011) What is a categorical model of arrows? Electronic Notes in Theoretical Computer Science, 229 (5). pp. 19-37. ISSN 1571-0661

[img]
Preview
PDF
arrows.pdf - Accepted Author Manuscript

Download (288kB) | Preview

Abstract

We investigate what the correct categorical formulation of Hughes’ Arrows should be. It has long been folklore that Arrows, a functional programming construct, and Freyd categories, a categorical notion due to Power, Robinson and Thielecke, are somehow equivalent. In this paper, we show that the situation is more subtle. By considering Arrows wholly within the base category we derive two alternative formulations of Freyd category that are equivalent to Arrows—enriched Freyd categories and indexed Freyd categories. By imposing a further condition, we characterise those indexed Freyd categories that are isomorphic to Freyd categories. The key differentiating point is the number of inputs available to a computation and the structure available on them, where structured input is modelled using comonads.