  A notion of general manifolds is introduced. It covers all usual manifolds in
mathematics. Essentially, it is a way how to get a bigger 'fibration' over a
site which locally coincides with a given one. An enrichment with generalized
elements is regarded which allows to see hom-sets of a given category as
(almost) objects and to transfer some technics from objects onto hom-sets.
Lifting problem for a group action and actions of group objects are also
included.
