Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Towards a taxonomy of atlases and of morphisms between them   Manifolds and fiber bundles, while superficially different, have strong
parallels; in particular, they are both defined in terms of equivalence classes
of atlases or in terms of maximal atlases, with the atlases treated as mere
adjuncts. This paper presents a unified view of atlases for manifolds and fiber
bundles as mathematical entities in their own right. It defines some convenient
notation, defines categories of atlases and defines functors among them.
  The paper "Local Coordinate Spaces: a proposed unification of manifolds with
fiber bundles, and associated machinery" (Arxiv:1801.05775) introduced some of
the ideas presented here, but many of the details are not needed there. This
paper fleshes out the concepts in more detail than would be relevant there.

20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph