Semi-tilting complexes

We introduce the notion of semi-tilting complexes, which is a small generalization of tilting complexes. Interesting examples include APR-semitilting complexes, etc. Note that non-trivial semi-tilting complexes exist for any non-semisimple non-local artin algebras, while tilting complexes may not. We extend interesting results in the tilting theory to semi-tilting complexes. As corollaries, we also obtain some new characterizations of tilting complexes.