# Constructing $A_\infty$-categories of matrix factorisations

## TL;DR

This paper develops explicit $A_
fty$-models for the DG-category of matrix factorizations over a commutative $Q$-algebra, enhancing the understanding of their algebraic structure.

## Contribution

It constructs Hom-finite $A_
fty$-categories with idempotent functors for matrix factorization DG-categories, providing a constructive approach.

## Key findings

- Explicit $A_
abla$-models for matrix factorization categories
- Hom-finite $A_
abla$-categories with idempotent functors
- Enhanced algebraic understanding of matrix factorizations

## Abstract

We study constructive $A_\infty$-models of the DG-category of matrix factorisations of a potential over a commutative $\mathbb{Q}$-algebra $k$, consisting of a Hom-finite $A_\infty$-category equipped with an $A_\infty$-idempotent functor.