8 papers
Convex Biproducts, Stochastic Matrices and Tape Diagrams
Filippo Bonchi, Cipriano Junior Cioffo
Categories with finite biproducts play a central role in category theory, providing an abstract setting in which additive and linear structures can be studied uniformly. In this pa…
Between Markov and restriction. Two more monads on categories for relations
Cipriano Junior Cioffo, Fabio Gadducci, Davide Trotta
The study of categories abstracting the structural properties of relations has been extensively developed over the years, resulting in a rich and diverse body of work. In a previou…
A taxonomy of categories for relations
Cipriano Junior Cioffo, Fabio Gadducci, Davide Trotta
The study of categories that abstract the structural properties of relations has been extensively developed over the years, resulting in a rich and diverse body of work. This paper…
Completeness for Probabilistic Boolean Tapes
Filippo Bonchi, Cipriano Junior Cioffo
Probabilistic Boolean circuits have recently been proposed as a string-diagrammatic foundation for finite probabilistic programming. In this paper, we present a complete set of axi…
Tapes as Stochastic Matrices of String Diagrams
Filippo Bonchi, Cipriano Junior Cioffo
Tape diagrams provide a graphical notation for categories equipped with two monoidal products, and , where is a biproduct. Recently, they have been gener…
Biased elementary doctrines and quotient completions
Cipriano Junior Cioffo
In this work, we fill the gap between the elementary quotient completion introduced by Maietti and Rosolini and the exact completion of a category with weak finite limits, as descr…