Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homotopy theory of complete Lie algebras and Lie models of simplicial
  sets   In a previous work, by extending the classical Quillen construction to the
non-simply connected case, we have built a pair of adjoint functors, 'model'
and 'realization', between the categories of simplicial sets and complete
differential graded Lie algebras. This paper is a follow up of this work. We
show that when X is a finite connected simplicial set, then the realization of
the model of X is the disjoint union of the Bousfield-Kan completion of X with
an external point. We also define a model category structure on the category of
complete differential graded algebras making the two previous functors a
Quillen pair, and we construct an explicit cylinder. In particular, these
functors preserve homotopies and weak equivalences and therefore, this gives
the basis for developing a Lie rational homotopy theory for all spaces.

14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom