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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 $\mathbb{Q}$.

Comparing commutative and associative unbounded differential graded algebras over $\mathbb{Q}$ from a homotopical point of view