# Enriched Sets and Higher Categories

## TL;DR

This paper introduces enriched sets as an abstraction of enriched categories, develops their categorical structure, and proposes a method for constructing and mapping between such enriched sets, advancing the theoretical framework of enriched category theory.

## Contribution

It defines enriched sets, constructs a category of these sets, and presents a method for building and relating enriched sets from given data, extending enriched category theory.

## Key findings

- Enriched sets form a new categorical abstraction.
- A category of enriched sets is established.
- A construction method for enriched sets and functors is proposed.

## Abstract

We introduce the notion of an enriched set, as an abstraction of enriched categories, and a category of enriched sets. The set of enriched sets is itself described as a set enriched over the category of enriched sets. We introduce a method for the construction of sets enriched over the set of enriched sets from a given enriched set with some addition data, and for "functors" from such enriched sets as should thereby arise to the enriched set of enriched sets.