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Book: CategoryTheory

See: Yoneda Lemma, Topos, Logic, Category theory glossary, Eduardo Ochs, Category theory obstacles, 20200524 Exercises, 20200705 Exercises



Higher Topos Theory

Natural transformations



Hidden assumptions

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 limits-colimits 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 relates God's outer perspective (on the general, external "black box" relationships) and our inner perspective, within the system, in terms of the properties of our particular system. The question of God's necessity and nature includes the relationship between God and human's perspectives.

Category theory expresses a duality between objects and mappings. Thus functors likewise have this dual nature, and so do natural transformations.


Category Theory Videos

Category Theory Books and Articles


For each object {$x$}, the identity morphism {${id}_x$} must be unique. Because consider {${id1}_x \circ {id2}_x$}. The identity is whichever disappears.

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.


Natural transformations

Adjoint functors


Relate id-A to consciousness, to constancy of attention, recurring attention.



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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