  Within the context of an involutive monoidal category the notion of a
comparison relation is identified. Instances are equality on sets, inequality
on posets, orthogonality on orthomodular lattices, non-empty intersection on
powersets, and inner product on vector or Hilbert spaces. Associated with a
collection of such (symmetric) comparison relations a dagger category is
defined with "tame" relations as morphisms. Examples include familiar
categories in the foundations of quantum mechanics, such as sets with partial
injections, or with locally bifinite relations, or with formal distributions
between them, or Hilbert spaces with bounded (continuous) linear maps. Of one
particular example of such a dagger category of tame relations, involving sets
and bifinite multirelations between them, the categorical structure is
investigated in some detail. It turns out to involve symmetric monoidal dagger
structure, with biproducts, and dagger kernels. This category may form an
appropriate universe for discrete quantum computations, just like Hilbert
spaces form a universe for continuous computation.
