  We develop a homotopy theory for additive categories endowed with
endofunctors, analogous to the concept of a model structure. We use it to
construct the homotopy theory of a Hovey triple (which consists of two
compatible complete cotorsion pairs) in an arbitrary exact category. We show
that the homotopy category of an exact model structure (in the sense of Hovey)
in a weakly idempotent complete exact category is equivalent to the subfactor
category of cofibrant-fibrant objects as pre-triangulated categories.
