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math.CT2024
On a fibrational construction for optics, lenses, and Dialectica categories
Matteo Capucci, Bruno GavranoviÄ, 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…
math.CT2024
Actegories for the Working Amthematician
Matteo Capucci, Bruno GavranoviÄ
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…
math.CT2024
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…