Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Representation theory of logics: a categorial approach   The major concern in the study of categories of logics is to describe
condition for preservation, under the a method of combination of logics, of
meta-logical properties. Our complementary approach to this field is study the
"global" aspects of categories of logics in the vein of the categories $\Ss,
\Ls, \cA_s$ studied in \cite{AFLM3}. All these categories have good properties
however the category of logics $\cL$ does not allow a good treatment of the
"identity problem" for logics (\cite{Bez}): for instance, the presentations of
"classical logics" (e.g., in the signature $\{\neg, \vee\}$ and
$\{\neg',\rightarrow'\}$) are not $\Ls$-isomorphic. In this work, we sketch a
possible way to overcome this "defect" (and anothers) by a mathematical device:
a representation theory of logics obtained from category theoretic aspects on
(Blok-Pigozzi) algebraizable logics. In this setting we propose the study of
(left and right) "Morita equivalence" of logics and variants. We introduce the
concepts of logics (left/right)-(stably) -Morita-equivalent and show that the
presentations of classical logics are stably Morita equivalent but classical
logics and intuitionist logics are not stably-Morita-equivalent: they are only
stably-Morita-adjointly related.

31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph