This lecture was given on March 12, 2018, at the Graduate Center of The City University of New York, during a session of the New York City Category Theory Seminar directed by Pr Noson S. Yanofsky, whom I warmly thank for the invitation. 

The reception of the participants was great, I keep a very good memory of this meeting !

N.B. : the last part of the lecture, about dynamics and interactivity, is extracted from a presentation given at the NIST (Gaithersburg, MD) on March 15, 2018, during a workshop on Applied Theory Category organized by Spencer Breiner.

Here are the slides (be patient, the slides may take a little time to load...)  :

Direct access to the slides :

• 1. General topology is not sufficient to study connectivity

  2. Connectivity structures of links

  3. Connectivity structures of multiple relations

  4. Connectivity structures of quantum entanglement

  5. Connectivity structures of families of random variables

  6. The topos of a connectivity space

  7. From links to dynamics : representations, foliations

  8. Functorial non-deterministic dynamics

  9. A general theory of interactivity

References