Cospan construction of the graph category of Borisov and Manin

TL;DR

This paper demonstrates how to derive the graph category of Borisov and Manin from a modified version of Joyal and Kock's graph category by reversing generic morphisms, representing morphisms as cospans.

Contribution

It introduces a new construction method for the Borisov-Manin graph category using cospans and morphism reversal, linking two existing graph category frameworks.

Findings

Borisov-Manin graph category can be obtained from Joyal-Kock's category via morphism reversal.

Morphisms are represented as cospans of reduced covers and refinement morphisms.

The construction clarifies the relationship between different graph categories.

Abstract

It is shown how the graph category of Borisov and Manin can be constructed from (a variant of) the graph category of Joyal and Kock, essentially by reversing the generic morphisms. More precisely, the morphisms in the Borisov-Manin category are exhibited as cospans of reduced covers and refinement morphisms.