Optics are bidirectional data accessors that capture data transformation patterns such as
accessing subfields or iterating over containers. Profunctor optics are a particular choice of …

We compare two possible ways of defining a category of 1-combs, the first intensionally as
coend optics and the second extensionally as a quotient by the operational behaviour of 1 …

Bayes' rule tells us how to invert a causal process in order to update our beliefs in light of
new evidence. If the process is believed to have a complex compositional structure, we may …

Optics are a data representation for compositional data access, with lenses as a popular
special case. Hedges has presented a diagrammatic calculus for lenses, but in a way that …

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 …

We define a categorical notion of cybernetic system as a dynamical realisation of a
generalized open game, along with a coherence condition. We show that this notion …

We further the theory of optics or" circuits-with-holes" to encompass premonoidal categories:
monoidal categories without the interchange law. Every premonoidal category gives rise to …

We identify morphisms of strong profunctors as a categorification of quantum supermaps.
These black-box generalisations of diagrams-with-holes are hence placed within the …

We study monoidal profunctors as a tool to reason and structure pure functional programs
both from a categorical perspective and as a Haskell implementation. From the categorical …

In this thesis of two Parts, we investigate the application of categorical methods to modelling
post-quantum theories. In Part I we study hyper-decoherence between quantum-like …