  Milner's bigraphs are a general framework for reasoning about distributed and
concurrent programming languages. Notably, it has been designed to encompass
both the pi-calculus and the Ambient calculus. This paper is only concerned
with bigraphical syntax: given what we here call a bigraphical signature K,
Milner constructs a (pre-) category of bigraphs BBig(K), whose main features
are (1) the presence of relative pushouts (RPOs), which makes them well-behaved
w.r.t. bisimulations, and that (2) the so-called structural equations become
equalities. Examples of the latter include, e.g., in pi and Ambient, renaming
of bound variables, associativity and commutativity of parallel composition, or
scope extrusion for restricted names. Also, bigraphs follow a scoping
discipline ensuring that, roughly, bound variables never escape their scope.
Here, we reconstruct bigraphs using a standard categorical tool: symmetric
monoidal closed (SMC) theories. Our theory enforces the same scoping discipline
as bigraphs, as a direct property of SMC structure. Furthermore, it elucidates
the slightly mysterious status of so-called links in bigraphs. Finally, our
category is also considerably larger than the category of bigraphs, notably
encompassing in the same framework terms and a flexible form of higher-order
contexts.
