Introduction to Abstract Homotopy Theory

TL;DR

This paper introduces abstract homotopy theory using model categories and $( abla,1)$-categories, aiming to show how classical homotopy theory can be understood more naturally through categorical frameworks.

Contribution

It provides an accessible introduction to abstract homotopy theory emphasizing categorical approaches without requiring prior categorical background.

Findings

Classical homotopy theory can be reformulated in categorical terms.

Model categories and $( abla,1)$-categories serve as foundational frameworks.

The approach simplifies understanding of homotopy concepts in topology.

Abstract

This is an introduction to the study of abstract homotopy theory by means of model categories and $(\infty,1)$-categories. The only prerequisites are very basic general topology and abstract algebra. None categorical background is needed. The final objective is to show that classical homotopy theory for topological spaces can be more naturally understood in terms of categorical language.