# Co-induced actions for topological and filtered groups

## TL;DR

This paper demonstrates that certain categories of topological and filtered groups are locally algebraically cartesian closed by establishing the existence of co-induced actions and functors, enhancing the understanding of their categorical structure.

## Contribution

It proves that the category of strongly central series admits co-induced actions and shows the existence of co-induction functors in topological groups, establishing new categorical properties.

## Key findings

- Category of strongly central series is LACC
- Existence of co-induction functors in topological groups
- A convenient category of topological groups is LACC

## Abstract

In this note, we show that the category of strongly central series admits co-induced actions, which means that it is Locally Algebraically Cartesian Closed. We also show that some co-induction functors exist in the category of topological groups, and that a convenient category of topological groups is LACC.