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