Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebraic models of non-connected spaces and homotopy theory of
  $L_\infty$ algebras   We develop a homotopy theory of $L_\infty$ algebras based on the
Lawrence-Sullivan construction, a complete differential graded Lie algebra
which, as we show, satisfies the necessary properties to become the right
cylinder in this category. As a result, we obtain a general procedure to
algebraically model the rational homotopy type of non-connected spaces.

15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys