Book

Math

Discovery

Andrius Kulikauskas

  • ms@ms.lt
  • +370 607 27 665
  • My work is in the Public Domain for all to share freely.

Lietuvių kalba

Understandable FFFFFF

Questions FFFFC0

Notes EEEEEE

Software

  • natural contradiction inherent in the approach of defining categories by starting with a category of categories and then taking a category to be its object
  • is there a category of universal properties?

Category Theory Videos

The Topos of Music: Geometric Logic of Concepts, Theory, and Performance. Guerino Mazzola.

From a Geometrical Point of View: A Study of the History and Philosophy of Category Theory (Logic, Epistemology, and the Unity of Science) Jean-Pierre Marquis

Categorical models for psychological consciousness. Sheaf theory - consciousness.

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.

I am thinking that categories should be considered on three levels:

  • Objects (of being - what is)
  • Arrows (of doing)
  • Equations (of reflecting) that relate arrows (or objects), especially in composition.

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.

Multiset is What, Set is How, List is Why. The reason that Set Theory works is that it is based on How, which is the level for all answers.

Yoneda lemma and the Foursome

  • Whether: object A (Accordion)
  • What: image F(A)
  • How: morphism from A: A->
  • Why: all morphisms to A: ->A

X (Xylophone)

Yoneda embedding: What=Why defines "meaning". What about other five qualities of signs?

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

Significant=unencompassable.

Covering=encompassing=Why.

Categorification (making math explicit) vs. Decategorification (making math implicit)

Algebraic combinatorics is the concrete flip-side of the abstractness of category theory. But algebraic combinatorics comes with implicit interpretation whereas category theory comes with explicit notation.

CategoryTheory


Naujausi pakeitimai


Puslapis paskutinį kartą pakeistas 2016 gruodžio 20 d., 21:22
Tweet