An extension of the Eilenberg - Mac Lane concept of category in the case of nonrigid structures

Nonrigid mathematical structures may no longer form usual Eilenberg - Mac Lane categories, but more general ones, as illustrated by pseudo-topologies. A rather general concept of pseudo-topology was used in constructing differential algebras of generalized functions containing the Schwartz distributions, [4-6,8-11]. These algebras proved to be convenient in solving large classes of nonlinear partial differential equations, see [12,13] and the literature cited there, as well as section 46F30 in the Subject Classification 2000 of the American Mathematical Society, at www.ams.org/index/msc/46Fxx.html The totality of such pseudo-topologies no longer constitutes a usual Eilenberg - Mac Lane category, but an extended one which is presented here. Other nonrigid mathematical structures are mentioned and treated briefly. This is a revised and augmented version of the earlier published paper [7].