to the construction of (adjacent) $t$-structures below.

In §\[sadjbrown\] we investigate the question when weight structures and $t$-structures admit (right or left) adjacent $t$-structures or weight structures (respectively); we also study adjacent “structures” if they exist. To prove the existence of these adjacent structures on a triangulated category ${\underline{C}}$ we usually assume a certain Brown representability-type condition for ${\underline{C}}$. We also recall the definition of perfect and symmetric classes and relate them to Brown-Comenetz duality and torsion pairs. This gives a funny (general) criterion for the existence of an adjacent torsion pair in terms of “symmetry” along with a “new” description of a $t$-structure that is right adjacent to a given compactly generated weight structure. In §\[spgtp\] we study compactly generated torsion pairs and perfectly generated weight structures; we prove several new and interesting results about them (and some of these statements were formulated above). In particular, we prove that for any “symmetric” ${\mathcal{P}},{\mathcal{P}}'\subset {\operatorname{Obj}}{\underline{C}}$ there exist adjacent $t$ and $w$ (co)generated by them. This implies the existence of a weight structure right adjacent to a given compactly generated $t$; hence the category ${{\underline{Ht}}}$ has an injective cogenerator and satisfies the AB3\* axiom. Combining this fact with the results of 