# Operads without coalgebras

## TL;DR

This paper presents an example of a linear operad with only trivial coalgebras and discusses conditions for the cofree coalgebra functor to be faithful, contributing to the understanding of operad-coalgebra relationships.

## Contribution

It introduces a non-trivial linear operad with trivial coalgebras and provides conditions for faithfulness of the cofree coalgebra functor.

## Key findings

- Existence of a non-trivial operad with only trivial coalgebras
- Conditions for the faithfulness of the cofree coalgebra functor
- Insights into operad and coalgebra structures

## Abstract

We give an example of a non-trivial linear operad that only admits trivial coalgebras and give sufficient conditions ensuring that the cofree coalgebra functor be faithful.

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Source: https://tomesphere.com/paper/1902.02551