We introduce monoidal streams: a generalization of causal stream functions to monoidal
categories. In the same way that streams provide semantics to dataflow programming with …

We study bicategories of (deterministic) automata, ie how automata $ E\leftarrow E\otimes
I\to O $ organise as the 1-cells of a bicategory $\mathbf {Mly} _\mathcal {K} $, drawing from …

Abstract We show that Span (Graph)∗, an algebra for open transition systems introduced by
Katis, Sabadini and Walters, satisfies a universal property. By itself, this is a justification of …

In recent years, a huge body of research has been devoted to the challenging problem of
integrating data and processes to achieve a more comprehensive understanding on their …

We introduce monoidal streams. Monoidal streams are a generalization of causal stream
functions, which can be defined in cartesian monoidal categories, to arbitrary symmetric …

We introduce monoidal width as a measure of complexity for morphisms in monoidal
categories. Inspired by well-known structural width measures for graphs, like tree width and …

We introduce monoidal width as a measure of the difficulty of decomposing morphisms in
monoidal categories. For graphs, we show that monoidal width and two variations capture …

We study the semibicategory $\textsf {Mre} $ of" Moore automata": an arrangement of
objects, 1-and 2-cells which is inherently and irredeemably nonunital in dimension one …

Explainable AI (XAI) aims to address the human need for safe and reliable AI systems.
However, numerous surveys emphasize the absence of a sound mathematical formalization …

We introduce effectful Mealy machines-a general notion of Mealy machine with global
effects-and give them semantics in terms of both effectful bisimilarity and traces. Bisimilarity …