See also: Community
The After Meetup
Every other Sunday I participate in the New York Category Theory Meetup study group on category theory. Afterwards, I stay for an informal dialogue with Wenbo Gao and others, which I dare call the "after meetup".
Some notes on our topics of interest
Category theory study group
- nyc-category-theory.slack.com
- Syd: What do we lose and gain from intutitionistic mathematics?
Categorial grammar
Francisco Varela
- Francisco Varela. Principles of Biological Autonomy. The Framework of Complementarity. Complementarity and adjunctions. Purpose.
- Adjunction: Every tree is a pointed graph inclusively. Then we can unfold a graph. A graph is a state machine. Draw which state is passing through.
- Category of graphs. Goguen and Varela.
- Radical constructivism. Mathematical construction. Autopoeisis. "The Tree of Knowledge".
- Louis Kauffman.
Memory Evolution Systems
- Ehresmann on Memory Evolution Systems. Neural systems. Cocones are superfundamental. Invariants. Limits.
- Categorical theory approach to neural networks. Weighted networks - sensory binding. Models of neural population dynamics. Time series oriented?
- MENS from Neurons to Higher Mental Processes to Consciousness. Ehresmann.
- Memory evolutive systems
Steven Philip
- Steven Philip. A category theory principle for cognitive science. Cognition - universal construction. Adjunction.
Yoneda Lemma
- Yoneda lemma - for understanding semantics. Distributional semantics. Words mean what they are associated with. Preceding words map to subsequent words.
- Identity function is related to object continuity discussed by Jean Piaget.
- Reflexive domain. {$\mathbb{C}\rightarrow\mathbb{C}$}
- Spivak. Adjoint functors. Summer school.
- Lenses. View update problem. Lens is a pointer to a specific thing.
- Synchronization. Build specification.
- Functional programming. Set the state, get the state. Want these functors to be well behaved. Structured data: XML document.
- Cylindric logic algebra. Monadic Boolean algebra.
- Open games. Game theory. Compositional equilibrium - adjunction? Communication.
Johannes
- Epistemology of cybernetics.