On Enriched Categories and Induced Representations

TL;DR

This paper demonstrates that induced representations for pairs of diffeological Lie groups can be constructed as indexed colimits within the category of diffeological spaces, expanding the understanding of representation theory in this context.

Contribution

It introduces a method to realize induced representations for diffeological Lie groups as indexed colimits, providing a new categorical approach.

Findings

Induced representations exist for pairs of diffeological Lie groups.

These representations can be constructed as indexed colimits in diffeological spaces.

The approach broadens the framework of representation theory in diffeological settings.

Abstract

We show that induced representations for a pair of $\textit{diffeological Lie groups}$ exist, in the form of an indexed colimit in the category of diffeological spaces.