Homotopy theory (nonfiction)

In mathematics, homotopy theory is a systematic study of situations in which maps come with homotopies between them. It originated as a topic in algebraic topology but nowadays it is studied as an independent discipline. Besides algebraic topology, the theory has also been in used in other areas of mathematics such as algebraic geometry (e.g., A¹ homotopy theory) and category theory (specifically the study of higher categories).