  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].
