Introduction

Our starting point is a particular “canvas” aimed to “draw” theories of physics, which has symmetric monoidal categories as its mathematical backbone. In this chapter, we consider the conceptual foundations for this canvas and how these can then be converted into mathematical structure.

With very little structural effort (i.e., in very abstract terms) and in a very short time span, the categorical quantum mechanics (CQM) research program, initiated by Abramsky and this author, has reproduced a surprisingly large fragment of quantum theory [3, 45, 48, 56, 60–62, 170, 179]. It also provides new insights both in quantum foundations and in quantum information—for example, in [49–51, 58, 59, 64, 79, 80]—and has even resulted in automated reasoning software called quantomatic [71–73], which exploits the deductive power of CQM, which is indeed a categorical quantum logic [77].

In this chapter, we complement the available material by not requiring prior knowledge of category theory and by pointing at connections to previous and current developments in the foundations of physics.

This research program is also in close synergy with developments elsewhere—for example, in representation theory [74], quantum algebra [176], knot theory [187], topological quantum field theory (TQFT) [132], and several other areas.