An elementary illustrated introduction to simplicial sets

TL;DR

This paper provides an accessible, illustrated introduction to simplicial sets and homotopy theory, emphasizing their combinatorial and geometric/topological connections for students with basic algebraic topology knowledge.

Contribution

It offers a clear, expository overview linking combinatorial and geometric aspects of simplicial sets for learners new to the subject.

Findings

Clarifies the relationship between combinatorial and topological aspects.

Provides illustrative explanations suitable for beginners.

Bridges the gap between abstract theory and geometric intuition.

Abstract

This is an expository introduction to simplicial sets and simplicial homotopy theory with particular focus on relating the combinatorial aspects of the theory to their geometric/topological origins. It is intended to be accessible to students familiar with just the fundamentals of algebraic topology.