Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strongly homotopy Lie algebras   The present paper can be thought of as a continuation of the paper
"Introduction to sh Lie algebras for physicists" by T. Lada and J. Stasheff
(International Journal of Theoretical Physics Vol. 32, No. 7 (1993),
1087--1103, appeared also as preprint hep-th/9209099) which provided an
exposition of the basic ingredients of the theory of strongly homotopy Lie
algebras sufficient for the underpinnings of the physically relevant examples.
We demonstrate the `strong homotopy' analog of the usual relation between Lie
and associative algebras and investigate the universal enveloping algebra
functor emerging as the left adjoint of the symmetrization functor. We show
that the category of homotopy associative algebras carries a natural monoidal
structure such that the universal enveloping algebra is a unital coassociative
cocommutative coalgebra with respect to this monoidal structure. The last
section is concerned with the relation between homotopy modules and weak
homotopy maps. The present paper is complementary to what currently exists in
the literature, both physical and mathematical.

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The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
3
The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: q-alg