2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115490A 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.37 pagesCategory TheoryGeneral Mathematics18Ftext