An Infinitary Model of Diagrammatic Calculus in Unbiased Monoidal Categories

Abstract: 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.