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All these points fail to mention that they are fundamentally self-relationship

Lawvere's fixed point theorem is I think the best formulation of the idea https://ncatlab.org/nlab/show/Lawvere%27s+fixed+point+theore...

I've been putting together a brain dump on the topic

https://github.com/adamnemecek/adjoint/

Join the discord

https://discord.gg/mr9TAhpyBW

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There's not really a connection here, the category of vector spaces isn't cartesian closed.

The category of Chu spaces is through.

No, it isn't. A star-autonomous cartesian category is just a preorder. Chu(Set, n) is star-autonomous but not a preorder, and therefore not cartesian. Or more concretely: cartesian categories are models for type systems with copying and deleting, but the Chu construction builds a model for a linear type system.

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