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Manifolds, Structures Categorically

G. V. Kondratiev
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Abstract

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.

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G. V. Kondratiev. 2006-08-20. Manifolds, Structures Categorically. https://arxiv.org/abs/math/0608503

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