A category of quantum categories

Quantum categories were introduced in [4] as generalizations of both bi(co)algebroids and small categories. We clarify details of that work. In particular, we show explicitly how the monadic definition of a quantum category unpacks to a set of axioms close to the definitions of a bialgebroid in the Hopf algebraic literature. We define notions of functor and natural transformation for quantum categories.Comment: Revised and expanded. A lot of diagrams. 40 page

Infrastructure for machine learning and computer vision

Dissertation presented as the partial requirement for obtaining a Master's degree in Data Science and Advanced AnalyticsThe infrastructure surrounding machine learning projects is of utmost importance: Machine learning projects require data acquisition mechanisms, software for data processing, as well as a benchmarking platform for evaluating performance of machine learning algorithms over time. In this report we describe our work aimed at developing such infrastructure for a Europe based computer vision startup specializing in human behaviour tracking. We discuss three projects comprising the work. One dedicated to creating a machine learning dataset for human behaviour monitoring, another to developing a screen-camera calibration tool, and third to setting up a benchmarking platform. The projects were integrated with the core technology of the startup, and will continue to be applied in the future.A infraestrutura para projetos de machine learning é de extrema importância para o desenvolvimento da tecnologia: exigem-se mecanismos de aquisição de dados, software para processamento de dados e uma plataforma de benchmarking para avaliar o desempenho de algoritmos de machine learning ao longo do tempo. No presente relatório, descreve-se o trabalho destinado a desenvolver essa infraestrutura para uma Startup Europeia de computer vision, especializada em rastreamento de comportamento humano atraves de câmeras de videos. Enfoca-se em três projetos que compõem o trabalho: o primeiro, dedicado à criação de um conjunto de dados de machine learning para monitoramento de comportamento humano; o segundo, sobre o desenvolvimento de uma ferramenta de calibração de câmeras e ecrã; e o terceiro, relata a criação de uma plataforma de benchmarking. Tais projetos foram integrados com a tecnologia central da Startup e serão aplicados no futuro

Representable (T,V)-categories

Working in the framework of $(\mathbb {T},\textbf {V})$-categories, for a symmetric monoidal closed category V and a (not necessarily cartesian) monad $\mathbb {T}$, we present a common account to the study of ordered compact Hausdorff spaces and stably compact spaces on one side and monoidal categories and representable multicategories on the other one. In this setting we introduce the notion of dual for $(\mathbb {T},\textbf {V})$-categories.Working in the framework of (T, V)-categories, for a symmetric monoidal closed category V and a (not necessarily cartesian) monad T, we present a common account to the study of ordered compact Hausdorff spaces and stably compact spaces on one side and monoidal categories and representable multicategories on the other one. In this setting we introduce the notion of dual for (T, V)-categories

Elements of enriched and quantum category theory

2 page(s