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

• 维基百科: Categorial grammar
• 维基百科: Linear logic
• 维基百科: N-gram

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.

Wenbo

• https://en.wikipedia.org/wiki/Boolean_satisfiability_problem participant
• Nicholas's interest: the mathematics of correlation, Pearson correlation matrix, discerning complicated structures
• Wenbo is interested in dialectical behavior. He is interested to learn topos theory to be able to apply Lawvere's interpretation of logic to express dialectical logic.
• How can structure arise that maintains itself?
• Foucault "The Order of Things".
• Oulipo. Kūryba pagal savo taisykles.
• Schelling požiūris panašus į mano, anot Wenbo.
• Yu-Gi-Oh! Trading card game.
• Embodied agency (video game). Valios įgyvendinimas.

Chinese

• http://blog.sina.com.cn/s/articlelist_1215048895_0_1.html
• http://blog.sina.com.cn/strongart
• https://space.bilibili.com/3182?from=search&seid=17518721354809687674

Peter

• Mazzola, Guerino. The Topos of Music Geometric Logic of Concepts, Theory, and Performance
• https://julesh.com/publications/
• https://arxiv.org/abs/1405.6881

Nicholas

• more robust measures of correlation
• Gazziniga Michael Gazzaniga. The Social Brain, Mind Matters, Nature's Mind, The Ethical Brain and Who's in Charge? Split-brain patients.

Category theory meetup

• https://www.amazon.com/Evolutive-Hierarchy-Emergence-Cognition-Multidisciplinarity/dp/0444522441