  We provide a unified framework to study hierarchies of relaxations for
Constraint Satisfaction Problems and their Promise variant. The idea is to
split the description of a hierarchy into an algebraic part, depending on a
minion capturing the "base level", and a geometric part - which we call
tensorisation - inspired by multilinear algebra. We exploit the geometry of the
tensor spaces arising from our construction to prove general properties of
hierarchies. We identify certain classes of minions, which we call linear and
conic, whose corresponding hierarchies have particularly fine features. We
establish that the (combinatorial) bounded width, Sherali-Adams LP, affine IP,
Sum-of-Squares SDP, and combined "LP + affine IP" hierarchies are all captured
by this framework. In particular, in order to analyse the Sum-of-Squares SDP
hierarchy, we also characterise the solvability of the standard SDP relaxation
through a new minion.
