  We define here the category of partial differential equations. Special cases
of morphisms from an object (equation) are symmetries of the equation and
reductions of the equation by a symmetry groups, but there are many other
morphisms. We are mostly interested in a subcategory that arises from second
order parabolic equations on arbitrary manifolds. We introduce a certain
structure in this category enabling us to find the simplest representative of
every quotient object of the given object, and develop a special-purpose
language for description and study of structures of this kind. An example that
deals with nonlinear reaction-diffusion equation is discussed in more detail.
