Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A global approach to AECs   In this work we present some general categorial ideas on Abstract Elementary
Classes (AECs) %\cite{She}, inspired by the totality of AECs of the form
$(Mod(T), \preceq)$, for a first-order theory T: (i) we define a natural notion
of (funtorial) morphism between AECs; (ii) explore the following constructions
of AECs: "generalized" theories, pullbacks of AECs, (Galois) types as AECs;
(iii) apply categorial and topological ideas to encode model-theoretic notions
on spaces of types %(see Michael Lieberman Phd thesis) ; (iv) present the
"local" axiom for AECs here called "local Robinson's property" and an
application (Robinson's diagram method); (v) introduce the category $AEC$ of
Grothendieck's gluings of all AECs (with change of basis); (vi) introduce the
"global" axioms of "tranversal Robinson's property" (TRP) and "global
Robinson's property" (GRP) and prove that TRP is equivalent to GRP and GRP
entails a natural version of Craig interpolation property.

7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga