Meaning of homotopy theory | Babel Free

Definitions

The systematic study of the situation of maps' having a homotopy between them; the study of equivalence classes (called homotopy classes) of maps.

countable, uncountable

Examples

“Homotopy theory originated as a topic in algebraic topology, but is now studied as an independent discipline in its own⟳ right, and as a tool in fields including category theory and algebraic geometry.”

“1988, Alex Heller, Homotopy Theories, American Mathematical Society, https://books.google.com.au/books?id=hkXUCQAAQBAJ&printsec=frontcover&dq=%22homotopy+theories%22&hl=en&newbks=1&newbks_redir=0&sa=X&ved=2ahUKEwiAzeb7qKfsAhUayTgGHeEyBZQQ6AEwAHoECAAQAg#v=onepage&q=%22homotopy%20theories%22&f=false.”

“This is our main result⟳, deduced from the axioms of a cofibration category, which leads to many new theorems on the homotopy classification problems in topology and in various algebraic homotopy theories.”

“They are also, from the viewpoint of homotopy theory, models for the homotopy theory of homotopy theories.”

CEFR level