We have followed two largely independent lines of thought, one philosophical and one mathematical. The overall proposal of diagrammatic immanence is meant to chart their possible long-term convergence. Immanent metaphysics has been characterised as intrinsically relational (Spinoza), semiotic (Peirce) and differential (Deleuze). Because diagrams – understood in a sufficiently broad sense – investigate relations by way of expressing relations and experimenting semiotically with differences, diagrams suggest themselves as a very general philosophical method conforming to the requirements of immanence. In elaborating the basic concepts of category theory we have uncovered a highly developed and extremely general field of mathematics that both uses its own type of diagrams as a formal notation and is also particularly adept at tracking how diagrams in general work. The schema of diagrammatic signification expressed in terms of the triad selection-experimentation-evaluation has served as a common locus, an overlap, of the philosophical and mathematical territories explored. As a schema expressible both in terms of Peirce's triadic theory of signs and as a category theoretical construction based in presheaves, it strongly suggests that further coordination along similar lines is possible. No doubt the formal constructions of adjunctions and topoi will be useful in testing this hypothesis. In any case, the pragmatic criterion remains crucial. As an entwined philosophical and mathematical approach to thinking in diagrams, what can diagrammatic immanence potentially do?

First of all, by shifting philosophical terrain both substantively and methodologically from language and textuality to diagrammatic relations and practices, an opening is made for enabling new constructive relations within philosophy itself and between philosophy and a variety of other fields. Obviously, the present proposal sets up multiple ways for metaphysics, formal logic and contemporary mathematics to communicate. In this respect, the present proposal may be broadly aligned with recent work by Badiou, Williamson, Zalamea and others, opening such work to productive dialogue with the Spinozist, Peircean and Deleuzian traditions in particular. But category theory is of course not just a tool for philosophers. It applies in its own distinctive manner to virtually any system of relations.