Algebraic Theories in Homotopy Theory
نویسندگان
چکیده
منابع مشابه
Algebraic Topology Notes: Homotopy Theory
Notes on homotopy theory, the first part of a trilogy on algebraic topology. Any typos, errors, mistakes, gaffes, etc., are entirely my folly.
متن کاملAlgebraic Homotopy Theory, Groups, and K-Theory
A thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy in The Faculty of Graduate Studies Department of Mathematics. LetMk be the category of algebras over a unique factorization domain k, and let ind−Affk denote the category of pro-representable functions from Mk to the category E of sets. It is shown that ind−Affk is a closed model category in such...
متن کاملAlgebraic K-theory and Abstract Homotopy Theory
We decompose the K-theory space of a Waldhausen category in terms of its Dwyer-Kan simplicial localization. This leads to a criterion for functors to induce equivalences of K-theory spectra that generalizes and explains many of the criteria appearing in the literature. We show that under mild hypotheses, a weakly exact functor that induces an equivalence of homotopy categories induces an equiva...
متن کاملReal Homotopy Theory of Semi-algebraic Sets
We complete the details of a theory outlined by Kontsevich and Soibelman that associates to a semi-algebraic set a certain graded commutative differential algebra of “semi-algebraic differential forms” in a functorial way. This algebra encodes the real homotopy type of the semialgebraic set in the spirit of the DeRham algebra of differential forms on a smooth manifold. Its development is needed...
متن کاملElements of a theory of algebraic theories
Kleisli bicategories are a natural environment in which the combinatorics involved in various notions of algebraic theory can be handled in a uniform way. The setting allows a clear account of comparisons between such notions. Algebraic theories, symmetric operads and nonsymmetric operads are treated as examples.
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ژورنال
عنوان ژورنال: The Annals of Mathematics
سال: 2002
ISSN: 0003-486X
DOI: 10.2307/3062135