Ind-affine schemes over an algebraically closed field k are introduced. The cone functor is then defined and characterized in the based category (ind-aff)* of ind-affine schemes. Homotopy theories, one induced from the monad related to the cone functor and the other via unirational and then singular simplices, are compared. Some homotopy groups vis-a-vis (ind-aff)* taking as our model of the circle the set of points (x,y) in k2satisfying x2+y2= 1 are determined.