Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The cone length and category of maps: pushouts, products and fibrations   For any collection of spaces A, we investigate two non-negative integer
homotopy invariants of maps: l_A(f), the A-cone length of f, and L_A(f), the
A-category of f. When A is the collection of all spaces, these are the cone
length and category of f, respectively, both of which have been studied
previously. The following results have been obtained: (1) For a map of one
homotopy pushout diagram into another, we derive an upper bound for I_A and L_A
of the induced map of homotopy pushouts in terms of I_A and L_A of the other
maps. This has many applications including an inequality for I_A and L_A of the
maps in a mapping of one mapping cone sequence into another. (2) We establish
an upper bound for I_A and L_A of the product of two maps in terms of I_A and
L_A of the given maps and the A-cone length of their domains. (3) We study our
invariants in a pullback square and obtain as a consequence an upper bound for
the A-cone length and A-category of the total space of a fibration in terms of
the A-cone length and A-category of the base and fiber. We conclude with
several remarks, examples and open questions.

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The categories of this paper are: cs
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga