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See: Yoneda Lemma, Topos, Sets, Logic Study:
I'm trying to learn category theory because it is relevant for homotopy type theory and other areas of mathematics. But also I may be able to use it to model parts of my philosophy. Category theory concepts such as adjoints (least upper bounds, greatest lower bounds) and limitscolimits are actually concepts of analysis. Category theory externalizes the internal structure of mathematical objects. It reexpresses that internal structures in terms of constraints on external relationships between structures. Category theory expresses a duality between objects and mappings. Thus functors likewise have this dual nature, and so do natural transformations. Category Theory Videos
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Ideas
I am thinking that categories should be considered on three levels:
The composition of the arrows always seems to me underexplained. And that is where the different levels of equivalence become relevant. Also to be considered is whether an object should be thought of as an arrow to itself. Adjoint functors Examples
Relate idA to consciousness, to constancy of attention, recurring attention. Significant=unencompassable. Covering=encompassing=Why. Computation trinitarianism takes as equivalent a proof of a proposition, a program with output of some type, and a generalized element of some object. 
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