  Properties of morphisms represented by so-called 'string diagrams' of
monoidal categories (and their braided and symmetric derivatives), mainly their
resistance in value to isotopic deformation, have made the usage of graphical
calculi commonplace in category theory ever since the correspondence between
diagrams and tensor categories was rigorously established by Joyal and Street
in 1991. However, we find it important to make certain additions to the
existing theory of monoidal categories and their diagrams, with the goal of
extending to so-called 'infinitary monoidal categories'. Most crucially, we
employ a structure inherently resistant to isotopic deformation, thus replacing
topological details with categorical ones. In the process, we coherently
introduce infinitary tensor product and transfinite composition into the
diagrammatic formalism.
