Synthetic differential geometry within homotopy type theory I

TL;DR

This paper initiates the development of synthetic differential geometry within homotopy type theory, establishing foundational concepts and setting the stage for future work on its model theory.

Contribution

It introduces the first steps towards integrating synthetic differential geometry into homotopy type theory, providing a foundational framework for further exploration.

Findings

Preliminary framework for synthetic differential geometry in homotopy type theory

Lays groundwork for future model-theoretic analysis

Establishes initial concepts for the integration of these fields

Abstract

This paper gives a first step towards developing synthetic differential geometry within homotopy type theory. Its model theory will be discussed in a subsequent paper.