Category Theory or: How to live without elements, using arrows instead (Part II)

Jun. 26, 2023

In the preceding post, we did a rudimentary survey of the principal elements comprising the apparatus of category theory. Henceforth, we shall direct our gaze towards the intricate constituents conjured by these foundational elements, plunging further into the intricate labyrinth of interwoven components in the machinery of category theory.

Table of Contents

Higher Category Theory

Higher category theory deals with the generalization of parts that make up machinery. In this realm, we erect structures in a context where, between objects, we have not only mere morphisms but k-morphisms, which are maps between (k - 1) of those morphisms where \(k \in \mathbb{N}\).

Cat : Category of small categories

2 Category

Universal Construction

Universal Property

Example of Universal Property



Equivalence of Categories Once more…


Example of Adjunctions

Curry in Haskell

Connections of Galois



Classical monoid

Category of Monoids


Examples of Monads

A Monad for moniod in the \(\textbf{Set}\)
Monads in Computer Science
Monads in Haskell
class Monad where
  return :: a -> m a
  (>>=)  :: m a -> (a -> m b) -> m b


The above material comes from my notes made while reading, watching,