  This is the first paper in a series where we generalize the Categorical
Quantum Mechanics program (due to Abramsky, Coecke, et al) to braided systems.
In our view a uniform description of quantum information for braided systems
has not yet emerged. The picture is complicated by a diversity of examples that
lacks a unifying framework for proving theorems and discovering new protocols.
  We use category theory to construct a high-level language that abstracts the
quantum mechanical properties of braided systems. We exploit this framework to
propose an axiomatic description of braided quantum information intended for
topological quantum computation.
  In this installment we first generalize the primordial Abramsky-Coecke
"quantum information flow" paradigm from compact closed categories to
right-rigid strict monoidal categories. We then study dagger structures for
rigid and/or braided categories and formulate a graphical dagger calculus. We
then propose two generalizations of strongly compact closed categories. Finally
we study partial traces in the context of dagger categories.
