# Free constructions and coproducts of d-frames

## TL;DR

This paper explores the theory of presentations for d-frames, identifies challenges, and establishes conditions under which the category of d-frames is closed under coproducts, advancing the structural understanding of d-frames.

## Contribution

It provides sufficient conditions for presentations of d-frames and proves that the category of d-frames is closed under coproducts, addressing gaps in the existing theory.

## Key findings

- Identified difficulties in presenting d-frames.
- Established conditions for overcoming these difficulties.
- Proved the category of d-frames is closed under coproducts.

## Abstract

A general theory of presentations for d-frames does not yet exist. We review the difficulties and give sufficient conditions for when they can be overcome. As an application we prove that the category of d-frames is closed under coproducts.