Comparing commutative and associative unbounded differential graded algebras over Q from homotopical point of view

TL;DR

This paper explores the homotopical relationship between certain categories of unbounded differential graded commutative and associative algebras over the rationals, establishing a faithfulness result.

Contribution

It introduces a homotopical faithfulness result connecting subcategories of CDGA and DGA over , advancing understanding of their structural similarities.

Findings

Established a faithfulness result in a homotopical sense

Connected subcategories of CDGA and DGA over 

Enhanced understanding of algebraic structures over 

Abstract

In this paper we establish a faithfulness result, in a homotopical sense, between a subcategory of the model category of augmented differential graded commutative algebras CDGA and a subcategory of the model category of augmented differential graded algebras DGA over the field of rational numbers $\mathbb{Q}$.