Escrows are optics

TL;DR

This paper offers a categorical framework for modeling escrow trading protocols, representing them as morphisms in the category of optics, and extends the model to more complex escrows with intermediaries using monoid and comonoid structures.

Contribution

It introduces a novel categorical interpretation of escrows as morphisms in the category of optics, enabling formal analysis of trustless trading protocols.

Findings

Escrows modeled as morphisms in the category of optics.

Extended models incorporate intermediaries using monoid and comonoid structures.

Provides a formal categorical foundation for escrow protocols.

Abstract

We provide a categorical interpretation for escrows, i.e. trading protocols in trustless environment, where the exchange between two agents is mediated by a third party where the buyer locks the money until they receive the goods they want from the seller. A simplified escrow system can be modeled as a certain kind of morphism in the category of optics on a monoidal category. When objects in the base category have monoid and comonoid structures, more involved kinds of escrows `with intermediaries' can be modelled as morphisms with action-like properties.