  We define tilting subcategories in arbitrary exact categories to archieve the
following. Firstly: Unify existing definitions of tilting subcategories to
arbitrary exact categories. Discuss standard results for tilting subcategories:
Auslander correspondence, Bazzoni description of the perpendicular category.
Secondly: We treat the question of induced derived equivalences separately -
given a tilting subcategory T, we ask if a functor on the perpendicular
category induces a derived equivalence to a (certain) functor category over T.
If this is the case, we call the tilting subcategory ideq tilting. We prove a
generalization of Miyashita's theorem (which is itself a generalization of a
well-known theorem of Brenner-Butler) and characterize exact categories with
enough projectives allowing ideq tilting subcategories. In particular, this is
always fulfilled if the exact category is abelian with enough projectives.
