Representable (T, V)-categories

TL;DR

This paper develops a unified framework for studying various categories such as ordered compact Hausdorff spaces and monoidal categories using $(T, V)$-categories, introducing a notion of duality within this setting.

Contribution

It introduces the concept of duals for $(T, V)$-categories, unifying different categorical structures under a common framework.

Findings

Unified approach to ordered compact Hausdorff and monoidal categories

Introduction of duality concept for $(T, V)$-categories

Framework applicable to various categorical structures

Abstract

Working in the framework of $(T, V)$-categories, for a symmetric monoidal closed category $V$ and a (not necessarily cartesian) monad $T$, we present a common account to the study of ordered compact Hausdorff spaces and stably compact spaces on one side and monoidal categories and representable multicategories on the other one. In this setting we introduce the notion of dual for $(T, V)$-categories.