19 citations · 61 across the 10 of their papers we have counts for
11 papers
The Produoidal Algebra of Process Decomposition
Matt Earnshaw, James Hefford, Mario Román
We introduce the normal produoidal category of monoidal contexts over an arbitrary monoidal category. In the same sense that a monoidal morphism represents a process, a monoidal co…
Evidential Decision Theory via Partial Markov Categories
Elena Di Lavore, Mario Román
We introduce partial Markov categories. In the same way that Markov categories encode stochastic processes, partial Markov categories encode stochastic processes with constraints,…
Coinductive Streams in Monoidal Categories
Elena Di Lavore, Giovanni de Felice, Mario Román
We introduce monoidal streams. Monoidal streams are a generalization of causal stream functions, which can be defined in cartesian monoidal categories, to arbitrary symmetric monoi…
Promonads and String Diagrams for Effectful Categories
Mario Román
Premonoidal and Freyd categories are both generalized by non-cartesian Freyd categories: effectful categories. We construct string diagrams for effectful categories in terms of the…
Monoidal Streams for Dataflow Programming
Elena Di Lavore, Giovanni de Felice, Mario Román
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 pure…
Span(Graph): a Canonical Feedback Algebra of Open Transition Systems
Elena Di Lavore, Alessandro Gianola, Mario Román +2
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 t…
Functorial Language Games for Question Answering
Giovanni de Felice, Elena Di Lavore, Mario Román +1
We present some categorical investigations into Wittgenstein's language-games, with applications to game-theoretic pragmatics and question-answering in natural language processing.
Open Diagrams via Coend Calculus
Mario Román
Morphisms in a monoidal category are usually interpreted as processes, and graphically depicted as square boxes. In practice, we are faced with the problem of interpreting what non…
Comb Diagrams for Discrete-Time Feedback
Mario Román
The data for many useful bidirectional constructions in applied category theory (optics, learners, games, quantum combs) can be expressed in terms of diagrams containing "holes" or…
Profunctor optics and traversals
Mario Román
Optics are bidirectional accessors of data structures; they provide a powerful abstraction of many common data transformations. This abstraction is compositional thanks to a repres…
Profunctor Optics, a Categorical Update
Bryce Clarke, Derek Elkins, Jeremy Gibbons +4
Optics are bidirectional data accessors that capture data transformation patterns such as accessing subfields or iterating over containers. Profunctor optics are a particular choic…