  In work of Fokkinga and Meertens a calculational approach to category theory
is developed. The scheme has many merits, but sacrifices useful type
information in the move to an equational style of reasoning. By contrast,
traditional proofs by diagram pasting retain the vital type information, but
poorly express the reasoning and development of categorical proofs. In order to
combine the strengths of these two perspectives, we propose the use of string
diagrams, common folklore in the category theory community, allowing us to
retain the type information whilst pursuing a calculational form of proof.
These graphical representations provide a topological perspective on
categorical proofs, and silently handle functoriality and naturality conditions
that require awkward bookkeeping in more traditional notation.
  Our approach is to proceed primarily by example, systematically applying
graphical techniques to many aspects of category theory. We develop string
diagrammatic formulations of many common notions, including adjunctions,
monads, Kan extensions, limits and colimits. We describe representable functors
graphically, and exploit these as a uniform source of graphical calculation
rules for many category theoretic concepts. These graphical tools are then used
to explicitly prove many standard results in our proposed diagrammatic style.
