111 citations · 374 across the 31 of their papers we have counts for
6 papers · 1 filter
String Diagram Rewrite Theory III: Confluence with and without Frobenius
Filippo Bonchi, Fabio Gadducci, Aleks Kissinger +2
In this paper we address the problem of proving confluence for string diagram rewriting, which was previously shown to be characterised combinatorically as double-pushout rewriting…
Convexity via Weak Distributive Laws
Filippo Bonchi, Alessio Santamaria
We study the canonical weak distributive law of the powerset monad over the semimodule monad for a certain class of semirings containing, in particular, positive semifields. Fo…
On Doctrines and Cartesian Bicategories
Filippo Bonchi, Alessio Santamaria, Jens Seeber +1
We study the relationship between cartesian bicategories and a specialisation of Lawvere's hyperdoctrines, namely elementary existential doctrines. Both provide different ways of a…
Diagrammatic Polyhedral Algebra
Filippo Bonchi, Alessandro Di Giorgio, Pawel Sobocinski
We extend the theory of Interacting Hopf algebras with an order primitive, and give a sound and complete axiomatisation of the prop of polyhedral cones. Next, we axiomatise an affi…
String Diagram Rewrite Theory II: Rewriting with Symmetric Monoidal Structure
Filippo Bonchi, Fabio Gadducci, Aleks Kissinger +2
Symmetric monoidal theories (SMTs) generalise algebraic theories in a way that make them suitable to express resource-sensitive systems, in which variables cannot be copied or disc…
Combining Semilattices and Semimodules
Filippo Bonchi, Alessio Santamaria
We describe the canonical weak distributive law of the powerset monad over the -left-semimodule monad $\ma…