For a differential graded k-quiver Q we define the free A_\infty-category FQ generated by Q. The main result is that the restriction A_\infty-functor A_\infty(FQ, A) \to A_1(Q,A) is an equivalence, where objects of the last A_\infty-category are morphisms of differential graded k-quivers Q \to A.
Keywords: A_\infty-categories, A_\infty-functors, A_\infty-transformations, 2-category, free A_\infty-category
2000 MSC: 18D05, 18D20, 18G55, 55U15
Theory and Applications of Categories,
Vol. 16, 2006,
No. 9, pp 174-205.
http://www.tac.mta.ca/tac/volumes/16/9/16-09.dvi
http://www.tac.mta.ca/tac/volumes/16/9/16-09.ps
http://www.tac.mta.ca/tac/volumes/16/9/16-09.pdf
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/16/9/16-09.dvi
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/16/9/16-09.ps