"homotopy theory" meaning in All languages combined

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