Related papers: A Simple Categorical Calculus of Interacting Proce…
We present a term rewriting system that models the dynamic aspects of the free cornering with protocol choice of a monoidal category, which has been proposed as a categorical model of process interaction. This term rewriting system is…
We extend the free cornering of a symmetric monoidal category, a double categorical model of concurrent interaction, to support branching communication protocols and iterated communication protocols. We validate our constructions by showing…
We present a unified framework for categorical systems theory which packages a collection of open systems, their interactions, and their maps into a symmetric monoidal loose right module of systems over a symmetric monoidal double category…
We present a process algebra aimed at describing interactions that are multiparty, i.e. that may involve more than two processes and that are open, i.e. the number of the processes they involve is not fixed or known a priori. Here we focus…
We present the MIM calculus, a modeling formalism with a strong biological basis, which provides biologically-meaningful operators for representing the interaction capabilities of molecular species. The operators of the calculus are…
We define a strongly normalising proof-net calculus corresponding to the logic of strongly compact closed categories with biproducts. The calculus is a full and faithful representation of the free strongly compact closed category with…
We develop a categorical approach to quivers and their modules. Naturally this leads to a notion of an action of a monoidal category on quivers. Using this, we construct for a large class of quivers rigid monoidal structures on their…
Monoidal computer is a categorical model of intensional computation, where many different programs correspond to the same input-output behavior. The upshot of yet another model of computation is that a categorical formalism should provide a…
Concurrent pattern calculus (CPC) drives interaction between processes by comparing data structures, just as sequential pattern calculus drives computation. By generalising from pattern matching to pattern unification, interaction becomes…
A coherent presentation of an n-category is a presentation by generators, relations and relations among relations. Confluent and terminating rewriting systems generate coherent presentations, whose relations among relations are defined by…
We introduce the wire calculus. Its dynamic features are inspired by Milner's CCS: a unary prefix operation, binary choice and a standard recursion construct. Instead of an interleaving parallel composition operator there are operators for…
The Functional Machine Calculus (Heijltjes 2022) is a new approach to unifying the imperative and functional programming paradigms. It extends the lambda-calculus, preserving the key features of confluent reduction and typed termination, to…
Circuit representations are becoming the lingua franca to express and reason about tractable generative and discriminative models. In this paper, we show how complex inference scenarios for these models that commonly arise in machine…
We show that the category of optics in a monoidal category arises naturally from the free cornering of that category. Further, we show that the free cornering of a monoidal category is a natural setting in which to work with comb diagrams…
Our starting point is a particular `canvas' aimed to `draw' theories of physics, which has symmetric monoidal categories as its mathematical backbone. In this paper we consider the conceptual foundations for this canvas, and how these can…
Differential categories are now an established abstract setting for differentiation. However not much attention has been given to the process which is inverse to differentiation: integration. This paper presents the parallel development for…
The Functional Machine Calculus (FMC), recently introduced by the authors, is a generalization of the lambda-calculus which may faithfully encode the effects of higher-order mutable store, I/O and probabilistic/non-deterministic input.…
With a view on applications in computing, in particular concurrency theory and higher-dimensional rewriting, we develop notions of $n$-fold monoid and comonoid objects in $n$-fold monoidal categories and bicategories. We present a series of…
Capture calculus has recently been proposed as a solution to effect checking, achieved by tracking the captured references of terms in the types. Boxes, along with the box and unbox operations, are a crucial construct in capture calculus,…
A symmetric monoidal category naturally arises as the mathematical structure that organizes physical systems, processes, and composition thereof, both sequentially and in parallel. This structure admits a purely graphical calculus. This…