Category theory log

Category I Category II Category III

1.1

Category theory is to Haskell what Haskell is to C++.

It makes certain things easier to express, such as concurrency.

Category theory abstracts over patterns we see in different paradigms.

E.g. lambda calculus, type theory, set theory, logic

Common way to describe all these.

As humans evolved, they needed to solve problems, e.g. hunting mammoths etc…

To do so, human minds evolved. We gained a world-view that things should be decomposable, and recomposable.

This allowed us to solve smaller problems and compose them back together.

However, in modern times as we apply this approach to various problems, we realize we may not be able to do so!

We expect that things break down into smaller and smaller particles until they become points (in physics), however soon enough we realize we can’t do so.

Things start behaving strangely (Quantum mechanics, String theory).

As such Category theory gives us a new perspective, about what behaviour we can observe, rather than how the internals look. e.g. epistomology vs ontology

1.2

Definition of Category

Primitives

Identity morphism

Composition

Objects

Function & sets as a Category