# $W$-Types in Categories of Coalgebras

## TL;DR

This paper develops a method to construct $W$-types within categories of coalgebras for cartesian comonads, extending previous constructions in presheaf and gluing toposes.

## Contribution

It introduces a generalized construction of $W$-types applicable to coalgebras for cartesian comonads, broadening the scope of existing theories.

## Key findings

- Constructed $W$-types in coalgebra categories for cartesian comonads
- Unified previous $W$-type constructions in presheaf and gluing toposes
- Extended the applicability of $W$-types in categorical frameworks

## Abstract

We construct $W$-types in the category of coalgebras for a cartesian comonad. It generalizes the constructions of $W$-types in presheaf toposes and gluing toposes.