Word Pronunciation & Dictionary

homotopy theory

Word Rarity Very rare

Frequency: Zipf frequency 2.18 in modern English

Syllables: ho-mo-topy- the-o-ry
IPA

30

Scrabble Score

14

Letters

6

Syllables

8

Unique Chars

Meaning

noun

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

Example Sentences

"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."

Usage

Inflected Forms

homotopy theories (plural)

Phrases

abstract homotopy theory A¹ homotopy theory rational homotopy theory fundamental group homotopy class homotopy group homotopy hypothesis

Frequently Paired Words

fundamental group homotopic homotopy class homotopy group homotopy hypothesis

Questions

What does homotopy theory mean?: The systematic study of the situation of maps' having a homotopy between them; the study of equivalence classes (called homotopy classes) of maps.

How to pronounce homotopy theory

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