# A Higher Structure Identity Principle

## TL;DR

This paper establishes a Structure Identity Principle for complex theories on types of h-level 3 within Univalent Foundations, using a novel notion of saturation for a broad class of definable structures.

## Contribution

It introduces a general saturation concept and proves a Structure Identity Principle for high-level types in Univalent Foundations, advancing the understanding of structural equivalences.

## Key findings

- Proves a Structure Identity Principle for h-level 3 types.
- Defines a new notion of saturation for structures.
- Applies to a broad class of structures in Univalent Foundations.

## Abstract

We prove a Structure Identity Principle for theories defined on types of $h$-level 3 by defining a general notion of saturation for a large class of structures definable in the Univalent Foundations.