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…
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…
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…
Tape Diagrams for Monoidal Monads
Filippo Bonchi, Cipriano Junior Cioffo, Alessandro Di Giorgio +1
Tape diagrams provide a graphical representation for arrows of rig categories, namely categories equipped with two monoidal structures, and , where dist…
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…
Fibred sets within a predicative and constructive effective topos
Cipriano Junior Cioffo, Maria Emilia Maietti, Samuele Maschio
We describe the fibrational structure of sets within the predicative variant of Hyland's Effective Topos previously introduced in Feferman's predicat…
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…