# Up-to-homotopy algebras with strict units. (Extended abstract version.)

## TL;DR

This paper establishes the existence of minimal models for operads with strict units, enabling a better understanding of up-to-homotopy algebras with strict units and providing a new proof of the formality of the unitary n-little disks operad.

## Contribution

It introduces minimal models for operads with nontrivial arity zero, advancing the theory of up-to-homotopy algebras with strict units.

## Key findings

- Existence of minimal models for operads with strict units.
- Up-to-homotopy algebras with strict units are operad algebras over these models.
- New proof of the formality of the unitary n-little disks operad over the rationals.

## Abstract

We prove the existence of minimal models a la Sullivan for operads with nontrivial arity zero. So up-to-homotopy algebras with strict units are just operad algebras over these minimal models. As an application, we give another proof of the formality of the unitary n-little disks operad over the rationals.