  We shall study the existence of almost split sequences in tri-exact
categories, that is, extension-closed subcategories of triangulated categories.
Our results unify and extend the existence theorems for almost split sequences
in abelian categories and exact categories (that is, extension-closed
subcategories of abelian categories), and those for almost split triangles in
triangulated categories. As applications, we shall obtain some new results on
the existence of almost split sequences in the derived categories of all
modules over an algebra with a unity or a locally finite dimensional algebra
given by a quiver with relations.
