# Quivers, Algebras and Adjoint functors

## TL;DR

This paper provides an accessible introduction to category theory and representation theory of finite-dimensional algebras, emphasizing the adjoint functor relationship between quivers and algebras with illustrative examples.

## Contribution

It introduces the concept of adjoint functors in the context of quivers and algebras, highlighting their categorical relationship with minimal proofs and practical examples.

## Key findings

- Quiver and algebra constructions form a pair of adjoint functors.
- The notes clarify basic notions of category theory and representation theory.
- Examples and exercises enhance understanding of theoretical concepts.

## Abstract

These are the notes for a minicourse held in Odessa (2016) and Belo Horizonte (2017). My aim was to provide a short introduction to basic notions of category theory and representation theory of finite-dimensional algebras. We learnt the concept of adjoint functors and showed that the construction "quiver" <-> "algebra" can be interpreted as a pair of adjoint functors between certain categories. Lectures almost do not contain the proofs, theoretical part is accompanied with examples, and sometimes introduced in the form of exercises.