  We introduce a notion of compatibility between constraint encoding and
compositional structure. Phrased in the language of category theory, it is
given by a "composable constraint encoding". We show that every composable
constraint encoding can be used to construct an equivalent notion of a
constrained category in which morphisms are supplemented with the constraints
they satisfy. We further describe how to express the compatibility of
constraints with additional categorical structures of their targets, such as
parallel composition, compactness, and time-symmetry. We present a variety of
concrete examples. Some are familiar in the study of quantum protocols and
quantum foundations, such as signalling and sectorial constraints; others arise
by construction from basic categorical notions. We use the language developed
to discuss the notion of intersectability of constraints and the
simplifications it allows for when present, and to show that any time-symmetric
theory of relational constraints admits a faithful notion of intersection.
