Phrase guide

homotopy theory

noun · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

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1

noun

Meaning 1

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

Definition source: English Wiktionary via Wiktextract

Usage: countable, uncountable

Topics: mathematics, sciences

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.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

No etymology was provided for this word.