# The tensor functor from the category of $A_\infty$-algebras into the category of differential modules with $\infty$-simplicial faces

## TL;DR

This paper constructs a tensor functor from the category of $A_
abla$-algebras to differential modules with $
abla$-simplicial faces, preserving homotopy equivalences, advancing the understanding of algebraic structures in homotopy theory.

## Contribution

It introduces a new tensor functor linking $A_
abla$-algebras and differential modules with $
abla$-simplicial faces, preserving homotopy equivalences.

## Key findings

- The tensor functor is explicitly constructed.
- Homotopy equivalences are preserved under the functor.
- The work advances the algebraic understanding of $
abla$-simplicial structures.

## Abstract

The tensor functor from the category of $A_\infty$-algebras into the category of differential modules with $\infty$-simplicial faces is constructed. Further, it is showed that this functor sends homotopy equivalent $A_\infty$-algebras into homotopy equivalent differential modules with $\infty$-simplicial faces.