Categorical Reconstruction Theory

TL;DR

This paper extends classical algebraic reconstruction results by employing advanced categorical frameworks like monads, monoidal categories, and duality notions, providing a more general and abstract understanding.

Contribution

It introduces a generalized categorical approach to algebraic reconstruction, incorporating monads, dualities, and module categories for broader applicability.

Findings

Unified categorical framework for algebraic reconstruction

Incorporation of duality notions such as closedness and rigidity

Generalization of classical results using monoidal categories

Abstract

We generalise classical reconstruction results in algebra, using the language of monads, monoidal categories, module categories, as well as various notions of duality, such as closedness, Grothendieck--Verdier duality (also known as *-autonomy), and rigidity.