  In this paper we study the question of how to transfer homotopic structure
from the category sD of simplicial objects in a fixed category D to D. To this
end we use a sort of homotopy colimit s : sD --> D, which we call simple
functor. For instance, the Bousfield-Kan homotopy colimit in a Quillen
simplicial model category is an example of simple functor. As a remarkable
example outside the setting of Quillen models we include Deligne simple of
mixed Hodge complexes. We prove here that the simple functor induces an
equivalence on the corresponding localized categories. We also describe a
natural structure of Brown category of cofibrant objects on sD. We use these
facts to produce cofiber sequences on the localized category of D by E, which
give rise to a natural Verdier triangulated structure in the stable case.
