22 citations · 41 across the 8 of their papers we have counts for
9 papers
A Fibrational Theory of First Order Differential Structures
Matteo Capucci, Geoffrey S. H. Cruttwell, Neil Ghani +1
We develop a categorical framework for reasoning about abstract properties of differentiation, based on the theory of fibrations. Our work encompasses the first-order fragments of…
On a fibrational construction for optics, lenses, and Dialectica categories
Matteo Capucci, Bruno Gavranović, Abdullah Malik +2
Categories of lenses/optics and Dialectica categories are both comprised of bidirectional morphisms of basically the same form. In this work we show how they can be considered a sp…
Diegetic Representation of Feedback in Open Games
Matteo Capucci
We improve the framework of open games with agency by showing how the players' counterfactual analysis giving rise to Nash equilibria can be described in the dynamics of the game i…
Seeing double through dependent optics
Matteo Capucci
Tambara modules are strong profunctors between monoidal categories. They've been defined by Tambara in the context of representation theory, but quickly found their way in applicat…
Lenses for Composable Servers
Andre Videla, Matteo Capucci
We implement the semantics of server operations using parameterised lenses. They allow us to define endpoints and extend them using classical lens composition. The parameterised na…
Actegories for the Working Amthematician
Matteo Capucci, Bruno Gavranović
Actions of monoidal categories on categories, also known as actegories, have been familiar to category theorists for a long time, and yet a comprehensive overview of this topic see…
Fibre optics
Dylan Braithwaite, Matteo Capucci, Bruno Gavranović +2
Lenses, optics and dependent lenses (or equivalently morphisms of containers, or equivalently natural transformations of polynomial functors) are all widely used in applied categor…
Translating Extensive Form Games to Open Games with Agency
Matteo Capucci, Neil Ghani, Jérémy Ledent +1
We show open games cover extensive form games with both perfect and imperfect information. Doing so forces us to address two current weaknesses in open games: the lack of a notion…
Towards Foundations of Categorical Cybernetics
Matteo Capucci, Bruno Gavranović, Jules Hedges +1
We propose a categorical framework for processes which interact bidirectionally with both an environment and a 'controller'. Examples include open learners, in which the controller…