A CATEGORICAL CONSTRUCTION OF MINIMAL MODEL

Abstract

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.-homomorphi Article DOI: http://dx.doi.org/10.20319/mijst.2016.s11.4863 This work is licensed under the Creative Commons Attribution-Non-commercial 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc/4.0/ or send a letter to Creative Commons, PO Box 1866, Mountain View, CA 94042, USA.