Dictionary

homotopy theory en · NOUN

Meanings

1. (countable, uncountable) The systematic study of the situation of maps' having a homotopy between them; the study of equivalence classes (called homotopy classes) of maps.
   • 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.
   • They are also, from the viewpoint of homotopy theory, models for the homotopy theory of homotopy theories. 2010, Julia E. Bergner, “A Survey of (∞,1)-Categories”, in John C. Baez, J. Peter May, editors, Towards Higher Categories, Springer,, page 69:
   • 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. 1989, Hans Joachim Baues, Algebraic Homotopy, Cambridge University Press, page 371:
   • 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.

Forms

Deriveds

abstract homotopy theory · rational homotopy theory · A¹ homotopy theory

Relateds

homotopy hypothesis · fundamental group · homotopy class · homotopy group · homotopic