A CATEGORICAL CONSTRUCTION OF MINIMAL MODEL

Deleanu, Frei and Hilton have developed the notion of generalized Adams completion in a categorical context; they have also suggested the dual notion, namely, Adams cocompletion of an object in a category. The concept of rational homotopy theory was first characterized by Quillen. In fact in rational homotopy theory Sullivan introduced the concept of minimal model. In this note under a reasonable assumption, the minimal model of a 1-connected differential graded algebra can be expressed as the Adams cocompletion of the differential graded algebra with respect to a chosen set in the category of 1-connected differential graded algebras (in short d.g.a.'s) over the field of rationals andand d.g.a.-homomorphisms.