Why is Abstract Algebra important? I think it is related to logic, philosophy, Category Theory, and Mathematical Logic.

Ideas from Category Theory

In my mind, this is a more formal and categorical version of Building a knowledge graph in Logseq.

These notes are made up of nested blocks (i.e. bullet points). You can access a block directly by clicking the arrow on the right side of the block. In theory, this coulud be a way to link between different people’s notes (i.e. Knowledge Graphs), and have direct access to the block hierarchy in published notes the same way one does in Logseq. Long-term, I hope to use this system to add more semantic meaning to the linked connections between notes, and explore the possible ramifications of surfacing their underlying categorical structure.

A point about Category Theory

and somewhat related, Category Theory

Category Theory

Category Theory

A nod to Category Theory and Functional Programming

I study the ways personal and interpersonal systems can be made functional to improve cognitive simplicity, including borrowing ideas from Category Theory and other metamathematical ideas.

Category Theory

Future theoretical consideration: Ideally one would create a category out of their knowledge graph, and this way they a functor to translate their knowledge graph to another knowledge graph would be guaranteed to have proper composition and matched types.

Side note: I’m thinking about Category Theory and considering knowledge graphs to be categories and translations between them to be functors.

Category Theory

A point about Category Theory

here I am using the term Category Theory term functor to describe a (potentially lossy) translation between two “knowledge graphs”

These notes are made up of nested blocks (i.e. bullet points). You can access a block directly by clicking the arrow on the right side of the block. In theory, this coulud be a way to link between different people’s notes (i.e. Knowledge Graphs), and have direct access to the block hierarchy in published notes the same way one does in Logseq. Long-term, I hope to use this system to add more semantic meaning to the linked connections between notes, and explore the possible ramifications of surfacing their underlying categorical structure.

Inspired by Richard Southwell and Bartosz Milewski youtube lectures on Category Theory.

This is the power behind generalized theories like Category Theory

• Category Theory

Even if knowledge cannot be represented as a graph, it does seem like a lot can be represented as a Category Theory Category

I also think about this knowledge graph as eventually being a category, but that’s beyond the scope of this spec.

Category Theory

Has some structural similarities to Category Theory, where you abstract away the details of the individual objects in the category, and now only about the way they interact with each other.