  We give a completely formalized definition of a notion of " general manifold
". It turns out that " gluing data " form an equivalence-partially ordered set
(e-pos), which is a special instance of an ordered groupoid. We state and prove
reconstruction theorems, allowing to reconstruct general manifolds and their
mor-phisms from such gluing data. To describe morphisms between manifolds, the
notion of natural relations between groupoids is introduced, which emphasizes
the close analogy with natural transformations of general category theory.
