A CATEGORICAL CONSTRUCTION OF MINIMAL MODEL
DOI:
https://doi.org/10.20319/mijst.2016.s11.4863Keywords:
Category of Fractions, Calculus of Right Fractions, Grothendieck Universe, Adamscocompletion, Differential Graded Algebra, Minimal ModelAbstract
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 anobject 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 rationales and d.g.a.-homomorphisms
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