In this paper we elaborate a general homotopy-theoretic framework in which to
study problems of descent and completion and of their duals, codescent and
cocompletion. Our approach to homotopic (co)descent and to derived
(co)completion can be viewed as $\infty$-category-theoretic, as our framework
is constructed in the universe of simplicially enriched categories, which are a
model for $(\infty, 1)$-categories.