  This article combines the vocabulary of semiotics and category theory to
provide a formal analysis of visualization. It shows how familiar processes of
visualization fit the semiotic frameworks of both Saussure and Peirce, and
extends these structures using the tools of category theory to provide a
general framework for understanding visualization in practice, including:
relationships between systems, data collected from those systems, renderings of
those data in the form of representations, the reading of those representations
to create visualizations, and the use of those visualizations to create
knowledge and understanding of the system under inspection. The resulting
framework is validated by demonstrating how familiar information visualization
concepts (such as literalness, sensitivity, redundancy, ambiguity,
generalizability, and chart junk) arise naturally from it and can be defined
formally and precisely. This article generalizes previous work on the formal
characterization of visualization by, inter alia, Ziemkiewicz and Kosara and
allows us to formally distinguish properties of the visualization process that
previous work does not.
