Open AccessFrom Γ-spaces to algebraic theories
Author(s) -
Bernard Badzioch
Publication year - 2004
Publication title -
transactions of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.798
H-Index - 100
eISSN - 1088-6850
pISSN - 0002-9947
DOI - 10.1090/s0002-9947-04-03711-0
Subject(s) - mathematics , homotopy , rotation formalisms in three dimensions , algebraic number , type (biology) , algebra over a field , semantics (computer science) , pure mathematics , computer science , mathematical analysis , geometry , programming language , ecology , biology
The paper examines semi-theories, that is, formalisms of the type of the Γ \Gamma -spaces of Segal which describe homotopy structures on topological spaces. It is shown that for any semi-theory one can find an algebraic theory describing the same structure on spaces as the original semi-theory. As a consequence one obtains a criterion for establishing when two semi-theories describe equivalent homotopy structures.