Universal property, Group, Category, Abelian group, Morphism, Mathematics

String Diagrams for Optics

On Dec 21, 2020
@davidad shared
@bgavran3 As far how to do optics with plain monoidal categories, https://t.co/i8mznwdW81 develops optic diagrams in this generality and more. The definition of optics, and that they form a category (with standard "nesting" composition), doesn't depend on symmetry/braiding at all.
Open

String Diagrams for Optics Guillaume Boisseau University of Oxford, United Kingdom Abstract Optics are a data representation for compositional data access, with lenses as a popular special case. 2012 ACM Subject Classification Software and its engineering → Visual languages; Software and ...

arxiv.org
On Dec 21, 2020
@davidad shared
@bgavran3 As far how to do optics with plain monoidal categories, https://t.co/i8mznwdW81 develops optic diagrams in this generality and more. The definition of optics, and that they form a category (with standard "nesting" composition), doesn't depend on symmetry/braiding at all.
Open

String Diagrams for Optics

String Diagrams for Optics

String Diagrams for Optics Guillaume Boisseau University of Oxford, United Kingdom Abstract Optics are a data representation for compositional data access, with lenses as a popular special ...

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This paper develops a three phase compositional axiomatisation of CGT: (i) the first phase consists of selecting an arrow to represent the play/coplay structure of open games; (ii) the ...

Dioptics: a Common Generalization of Open Games and Gradient-Based Learners

Dioptics: a Common Generalization of  Open Games and Gradient-Based Learners

A1.1.5 Definition of a product category Program Definition Product (C1 C2 : Category) : Category := {| obj := obj C1 × obj C2; hom := fun x y 7→ ((hom C1 ( fst x) ( fst y)) × (hom C2 (snd ...

Category Theory

Category Theory

He achieved the following: Axiomatized the category of sets (Lawvere 1964) and of categories (Lawvere 1966); Gave a categorical description of theories that was independent of syntactical ...