iwilare / categorical-automata

Bicategories of automata, completeness of F-automata in monoidal categories, adjoints between (semi)bicategories; https://arxiv.org/pdf/2303.03867, https://arxiv.org/pdf/2303.03865, https://arxiv.org/abs/2305.00272

Categorical automata in Agda

This repository contains the Agda formalization for a series of papers by Guido Boccali, Andrea Laretto, Fosco Loregian, Stefano Luneia and Bojana Femić on categorical automata in monoidal and cartesian categories and how they are organized (semi)bicategorically.

• "Bicategories of automata, automata in bicategories" (https://arxiv.org/pdf/2303.03865.pdf)
• "Completeness for categories of generalized automata" (https://arxiv.org/pdf/2303.03867.pdf)
• "Semibicategories of Moore automata" (https://arxiv.org/abs/2305.00272)

Main formalization files

• Automata (Moore / Mealy) - definition of machines as spans in a cartesian category
• FMoore / FMealy - definition of F-machines, generalizing to endofunctors in the span
• Mealy/Bicategory: the bicategory of Mealy automata
• FMoore/Limits: terminal object and products in the category of F-Moore automata
• AsPullbacks: redirection to the definition of F-Moore and F-Mealy as strict pullbacks in Cat
• Set/* main development of "Semibicategories of Moore automata", using direct computations in Set

Requirements

• agda-categories 0.1.7.2
• agda-stdlib 1.7.2
• agda 2.6.3