19 citations · 40 across the 10 of their papers we have counts for
11 papers
The free bifibration on a functor
Bryce Clarke, Gabriel Scherer, Noam Zeilberger
We consider the problem of constructing the free bifibration generated by a functor of categories . This problem was previously considered by Lamarche, and is closely…
The Grothendieck construction for delta lenses
Bryce Clarke
Delta lenses are functors equipped with a functorial choice of lifts, generalising the notion of split opfibration. In this paper, we introduce a Grothendieck construction (or cate…
Lifting twisted coreflections against delta lenses
Bryce Clarke
Delta lenses are functors equipped with a suitable choice of lifts, generalising the notion of split opfibration. In recent work, delta lenses were characterised as the right class…
The Algebraic Weak Factorisation System for Delta Lenses
Bryce Clarke
Delta lenses are functors equipped with a suitable choice of lifts, and are used to model bidirectional transformations between systems. In this paper, we construct an algebraic we…
An introduction to enriched cofunctors
Bryce Clarke, Matthew Di Meglio
Cofunctors are a kind of map between categories which lift morphisms along an object assignment. In this paper, we introduce cofunctors between categories enriched in a distributiv…
Delta lenses as coalgebras for a comonad
Bryce Clarke
Delta lenses are a kind of morphism between categories which are used to model bidirectional transformations between systems. Classical state-based lenses, also known as very well-…
Limits and Colimits in a Category of Lenses
Emma Chollet, Bryce Clarke, Michael Johnson +3
Lenses are an important tool in applied category theory. While individual lenses have been widely used in applications, many of the mathematical properties of the corresponding cat…
A diagrammatic approach to symmetric lenses
Bryce Clarke
Lenses are a mathematical structure for maintaining consistency between a pair of systems. In their ongoing research program, Johnson and Rosebrugh have sought to unify the treatme…
Internal lenses as functors and cofunctors
Bryce Clarke
Lenses may be characterised as objects in the category of algebras over a monad, however they are often understood instead as morphisms, which propagate updates between systems. Wo…
Internal split opfibrations and cofunctors
Bryce Clarke
Split opfibrations are functors equipped with a suitable choice of opcartesian lifts. The purpose of this paper is to characterise internal split opfibrations through separating th…
Profunctor Optics, a Categorical Update
Bryce Clarke, Derek Elkins, Jeremy Gibbons +4
Optics are bidirectional data accessors that capture data transformation patterns such as accessing subfields or iterating over containers. Profunctor optics are a particular choic…