  In paper arXiv:1406.1744, we constructed a symmetric monoidal category
$LIE^{MC}$ whose objects are shifted (and filtered) L-infinity algebras. Here,
we fix a cooperad $C$ and show that algebras over the operad $Cobar(C)$
naturally form a category enriched over $LIE^{MC}$. Following arXiv:1406.1744,
we "integrate" this $LIE^{MC}$-enriched category to a simplicial category
$HoAlg^{\Delta}_C$ whose mapping spaces are Kan complexes. The simplicial
category $HoAlg^{\Delta}_C$ gives us a particularly nice model of an
$(\infty,1)$-category of $Cobar(C)$-algebras. We show that the homotopy
category of $HoAlg^{\Delta}_C$ is the localization of the category of
$Cobar(C)$-algebras and infinity morphisms with respect to infinity
quasi-isomorphisms. Finally, we show that the Homotopy Transfer Theorem is a
simple consequence of the Goldman-Millson theorem.
