On perfectly generated weight structures and adjacent t-structures

This paper is dedicated to the study of smashing weight structures (these are "coherent with coproducts"), and application their properties t-structures. In particular, we prove that hearts compactly generated t-structures Grothendieck abelian categories; this statement strengthens earlier results several other authors. The central theorem as follows: any perfect (as defined by Neeman) set objects a triangulated category generates structure; say obtained way perfectly generated. An important family (the opposites to) ones right adjacent t-structures; they give injective cogenerators for latter. Moreover, establish following not so explicit result: structure on well (this generalization notion was also generated; actually, more than that. Furthermore, classification torsion theories generalize both t-structures) extends corresponding result D. Pospisil J. Š?oví?ek arbitrary categories. gives t-structure due B. Keller P. Nicolas.