##  [Homotopy Theory](/homotopy-theory) 

  ##  [Homotopy Theory](https://puremath.quantumdictionary.io/homotopy-theory-0) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The study of topological spaces, maps, and constructions up to homotopy equivalence, together with algebraic and categorical structures (homotopy groups, model categories, spectra) that encode higher-dimensional deformation information.