  We develop a homotopy theoretical version of classical Morita theory using
the notion of a strong monad. It was Anders Kock who proved that a monad T in a
monoidal category E is strong if and only if T is enriched in E. We prove that
this correspondence between strength and enrichment follows from a
2-isomorphism of 2-categories. Under certain conditions on T, we prove that the
category of T-algebras is Quillen equivalent to the category of modules over
the endomorphism monoid of the T-algebra T(I) freely generated by the unit I of
E. In the special case where E is the category of Gamma-spaces equipped with
Bousfield-Friedlander's stable model structure and T is the strong monad
associated to a well-pointed Gamma-theory, we recover a theorem of Stefan
Schwede, as an instance of a general homotopical Morita theorem.
