# Second Statebox Summit

## Second Statebox Summit - The Netherlands

We hosted a two day Category Theory camp, 4 day research workshop, and a Meetup. Below are the videos which were produced during live streaming of the events.

You can find out more about the summit here.

## Open Petri Nets

### Jade Master

Jade goes through his paper in collaboration with John Baez about connecting Petri nets together.

## Cashing in on Statebox

### Josh Harvey

Josh, Lamassu co-founder, describes how Statebox is being used to make Lamassu's ATM code better.

## What are Visual Languages

### Stefano Gogioso

Stefano Gogioso, researcher at the University of Oxford Quantum Group, explains what are visual languages and diagrammatics.

## GET Protocol. What Smart Ticketing and Petri Nets Have in Common

### Sander Regtuijt

Sander from GUTS Tickets explains the inner workings of the tech behind their project, and how Statebox is helping to improve it.

## Gamification of Life

### Amin Rafiee

Amin does a big recap of how the blockchain scene changed from the early days to 2018, and how the approach to topics like privacy and ethics evolved within it.

## Ethical Computing and Natural Systems

### Matthew Schutte

Matthew from Holochain goes through the nature-inspired and ethical principles that are behind Holochain design.

## Law was Code before Code was Law

### Florian Glatz

Florian from Blockchain Embassy explores the similarities between code and law.

## Meetup Organizers of the World, Unite!

### Jana Petkanic

Jana from Blockchaintalks speaks about the responsibilities that people involved in organizing meetups and events have.

## Finally, a Money Theory and a Bank for Central Banks

### Viktor Winschel

Viktor talks about money theory and why it is so difficult.

## Journal announcement and panel discussion on visual programming

### Multiple speakers

The academic journal Statebox is helping to bootstrap is announced. A panel discussion about visual programming follows.

## Category Theory Camp - Definition of Category

### Fabrizio Genovese

The motivation between category theory is explained and categories are defined.

## Category Theory Camp - Op Categories, Functors

### Fabrizio Genovese

Dualities are defined, along with morphism of categories, functors.

## Category Theory Camp - Natural Transformations, Presheaves

### Fabrizio Genovese

Morphisms between functors, called natural transformations, are introduced. Presheaves are used as a case study.

## Category Theory Camp - Monads and Eilenberg-Moore algebras

### Fabrizio Genovese

As a case study of functors, categories and natural transformations, monads and their algebras are considered.

## Category Theory Camp - Products, Terminal Objects

### Fabrizio Genovese

The motivation behind limits is explained by recasting categorically the notion of cartesian product. Terminal objects are introduced.

## Category Theory Camp - Pullbacks, Diagram Functors

### Fabrizio Genovese

The methodology that allowed to define cartesian products is generalized to pullbacks. To explain how this works in full generality we start talking about category of shapes and diagram functors.

## Category Theory Camp - Cones, Limits

### Fabrizio Genovese

The notion of cone is defined. Limits are presented as terminal objects on cones.

## Category Theory Camp - Colimits, Initial F-Algebras

### Fabrizio Genovese

Dualizing the notion of limit, colimits are obtained. Initial F-Algebras are used as a case study to summarize the notions covered.

## Category Theory Camp - Monoidal Categories, Graphical Languages

### Fabrizio Genovese

Categorical products are weakened to monoidal categories. Symmetry is then introduced. Finally, the link betweeh monoidal categories and diagrammatic reasoning is summarized.

## Category Theory Camp - Monoids, Monads as Monoids, Monoidal Functors

### Fabrizio Genovese

Monoidal objects are defined. Monads are recasted as monoids on endofunctors of a category. Monoidal functors are defined.

## Category Theory Camp - Cospan Composition

### Fabrizio Genovese

As a case study, monoidal structure and pushouts are used to explain compositionality via cospan composition.

## Category Theory Camp - The Hom Functor and the Yoneda Lemma

### Fabrizio Genovese

The Hom functor is introduced, along with the Yoneda Lemma and its proof.

## Category Theory Camp - Subobject Classifiers

### Fabrizio Genovese

To show why the Yoneda Lemma is useful, subobject classifiers are defined and the lemma is applied to find the subobject classifier of a presheaf category.

## Category Theory Camp - Cartesian Closed Categories

### Fabrizio Genovese

The notion of product category is extended internalizing the hom functor, giving rise to the notion of cartesian closed category (CCC).

## Category Theory Camp - CCC as Models of Labda Calculus, Enriched Categories, Surface Diagrams

### Fabrizio Genovese

The Curry-Howard isomorphism between logic and computation is extended, showing how cartesian closed categories are models of lambda calculus.

## Category Theory Camp - The Grothendieck Construction

### Fabrizio Genovese

The Grothendieck construction is presented.