  The category of unital (unbounded) dg cocommutative coalgebras over a field
of characteristic zero is provided with a structure of simplicial closed model
category. This generalizes the model structure defined by Quillen in 1969 for
2-reduced coalgebras. In our case, the notion of weak equivalence is structly
stronger than that of quasi-isomorphism. A pair of adjoint functors connecting
the category of coalgebras with the category of dg Lie algebras, induces an
equivalence of the corresponding homotopy categories.
  The model category structure allows one to consider dg coalgebras as very
general formal stacks. The corresponding Lie algebra is then interpreted as a
tangent Lie algebra which defines the formal stack uniquely up to a weak
equivalence.
  An example of the coalgebra of formal deformaions of a principal $G$-bundle
on a scheme $X$ is calculated.
