The Experts below are selected from a list of 321 Experts worldwide ranked by ideXlab platform

Hernán J. San Martín - One of the best experts on this subject based on the ideXlab platform.

Justin Noel - One of the best experts on this subject based on the ideXlab platform.

  • LIFTING HOMOTOPY T-ALGEBRA MAPS TO STRICT MAPS
    2016
    Co-Authors: Niles Johnson, Justin Noel, E∞(σ∞+ Coker J Lk()r
    Abstract:

    ABSTRACT. The settings for homotopical algebra—categories such as simplicial groups, simplicial rings, A ∞ spaces, E ∞ ring spectra, etc.—are oftentimes equivalent to categories of algebras over some monad or triple T. In such cases, T is acting on a nice simplicial model category in such a way that the T descends to a monad on the homotopy category and defines a category of homotopy T-algebras. In this setting there is a Forgetful Functor from the homotopy category of T-algebras to the category of homotopy T-algebras. Under suitable hypotheses we provide an obstruction theory, in the form of a Bousfield-Kan spec-tral sequence, for lifting a homotopy T-algebra map to a strict map of T-algebras. Once we have a map of T-algebras to serve as a basepoint, the spectral sequence computes the homotopy groups of the space of T-algebra maps and the edge homomorphism on pi0 is the aforementioned Forgetful func-tor. We discuss a variety of settings in which the required hypotheses are satisfied, including monads arising from algebraic theories and from operads. We provide examples in G-spaces, G-spectra, rational E∞-algebras, and A∞-algebras under an Eilenberg-MacLane commutative ring spectrum. We give explicit calculations, connected to rational unstable homotopy theory, showing that the Forgetful Functor from the homotopy category of E∞ ring spectra to the category of H ∞ ring spectra is generally neither full nor faithful. We also apply a result of the second named author and Nick Kuhn to compute the homotopy type of the spac

  • Lifting homotopy T-algebra maps to strict maps
    Advances in Mathematics, 2014
    Co-Authors: Niles Johnson, Justin Noel
    Abstract:

    Abstract The settings for homotopical algebra—categories such as simplicial groups, simplicial rings, A ∞ spaces, E ∞ ring spectra, etc.—are often equivalent to categories of algebras over some monad or triple T. In such cases, T is acting on a nice simplicial model category in such a way that T descends to a monad on the homotopy category and defines a category of homotopy T-algebras. In this setting there is a Forgetful Functor from the homotopy category of T-algebras to the category of homotopy T-algebras. Under suitable hypotheses we provide an obstruction theory, in the form of a Bousfield–Kan spectral sequence, for lifting a homotopy T-algebra map to a strict map of T-algebras. Once we have a map of T-algebras to serve as a basepoint, the spectral sequence computes the homotopy groups of the space of T-algebra maps and the edge homomorphism on π 0 is the aforementioned Forgetful Functor. We discuss a variety of settings in which the required hypotheses are satisfied, including monads arising from algebraic theories and operads. We also give sufficient conditions for the E 2 -term to be calculable in terms of Quillen cohomology groups. We provide worked examples in G-spaces, G-spectra, rational E ∞ algebras, and A ∞ algebras. Explicit calculations, connected to rational unstable homotopy theory, show that the Forgetful Functor from the homotopy category of E ∞ ring spectra to the category of H ∞ ring spectra is generally neither full nor faithful. We also apply a result of the second named author and Nick Kuhn to compute the homotopy type of the space E ∞ ( Σ + ∞ Coker J , L K ( 2 ) R ) .

Niles Johnson - One of the best experts on this subject based on the ideXlab platform.

  • LIFTING HOMOTOPY T-ALGEBRA MAPS TO STRICT MAPS
    2016
    Co-Authors: Niles Johnson, Justin Noel, E∞(σ∞+ Coker J Lk()r
    Abstract:

    ABSTRACT. The settings for homotopical algebra—categories such as simplicial groups, simplicial rings, A ∞ spaces, E ∞ ring spectra, etc.—are oftentimes equivalent to categories of algebras over some monad or triple T. In such cases, T is acting on a nice simplicial model category in such a way that the T descends to a monad on the homotopy category and defines a category of homotopy T-algebras. In this setting there is a Forgetful Functor from the homotopy category of T-algebras to the category of homotopy T-algebras. Under suitable hypotheses we provide an obstruction theory, in the form of a Bousfield-Kan spec-tral sequence, for lifting a homotopy T-algebra map to a strict map of T-algebras. Once we have a map of T-algebras to serve as a basepoint, the spectral sequence computes the homotopy groups of the space of T-algebra maps and the edge homomorphism on pi0 is the aforementioned Forgetful func-tor. We discuss a variety of settings in which the required hypotheses are satisfied, including monads arising from algebraic theories and from operads. We provide examples in G-spaces, G-spectra, rational E∞-algebras, and A∞-algebras under an Eilenberg-MacLane commutative ring spectrum. We give explicit calculations, connected to rational unstable homotopy theory, showing that the Forgetful Functor from the homotopy category of E∞ ring spectra to the category of H ∞ ring spectra is generally neither full nor faithful. We also apply a result of the second named author and Nick Kuhn to compute the homotopy type of the spac

  • Lifting homotopy T-algebra maps to strict maps
    Advances in Mathematics, 2014
    Co-Authors: Niles Johnson, Justin Noel
    Abstract:

    Abstract The settings for homotopical algebra—categories such as simplicial groups, simplicial rings, A ∞ spaces, E ∞ ring spectra, etc.—are often equivalent to categories of algebras over some monad or triple T. In such cases, T is acting on a nice simplicial model category in such a way that T descends to a monad on the homotopy category and defines a category of homotopy T-algebras. In this setting there is a Forgetful Functor from the homotopy category of T-algebras to the category of homotopy T-algebras. Under suitable hypotheses we provide an obstruction theory, in the form of a Bousfield–Kan spectral sequence, for lifting a homotopy T-algebra map to a strict map of T-algebras. Once we have a map of T-algebras to serve as a basepoint, the spectral sequence computes the homotopy groups of the space of T-algebra maps and the edge homomorphism on π 0 is the aforementioned Forgetful Functor. We discuss a variety of settings in which the required hypotheses are satisfied, including monads arising from algebraic theories and operads. We also give sufficient conditions for the E 2 -term to be calculable in terms of Quillen cohomology groups. We provide worked examples in G-spaces, G-spectra, rational E ∞ algebras, and A ∞ algebras. Explicit calculations, connected to rational unstable homotopy theory, show that the Forgetful Functor from the homotopy category of E ∞ ring spectra to the category of H ∞ ring spectra is generally neither full nor faithful. We also apply a result of the second named author and Nick Kuhn to compute the homotopy type of the space E ∞ ( Σ + ∞ Coker J , L K ( 2 ) R ) .

José Luis Castiglioni - One of the best experts on this subject based on the ideXlab platform.

  • Prelinear Hilbert algebras
    Fuzzy Sets and Systems, 2020
    Co-Authors: José Luis Castiglioni, Sergio A. Celani, Hernán J. San Martín
    Abstract:

    Abstract In this paper we give an explicit description of the left adjoint of the Forgetful Functor from the algebraic category of Godel algebras (i.e., prelinear Heyting algebras) to the algebraic category of bounded prelinear Hilbert algebras. We apply this result in order to study possible descriptions of the coproduct of two finite algebras in the algebraic category of prelinear Hilbert algebras.

  • On prelinear Hilbert algebras with successor
    Fuzzy Sets and Systems, 2020
    Co-Authors: José Luis Castiglioni, Hernán J. San Martín
    Abstract:

    Abstract In this paper we give an explicit description of the left adjoint of the Forgetful Functor from the algebraic category of Godel algebras with successor to the algebraic category of bounded prelinear Hilbert algebras with successor. We apply this result in order to study possible descriptions of the coproduct of two finite algebras in the algebraic category of prelinear Hilbert algebras with successor.

  • On the free Heyting algebra extension of a Hilbert algebra
    arXiv: Logic, 2017
    Co-Authors: José Luis Castiglioni, Hernán J. San Martín
    Abstract:

    In this paper we provided an explicit construction for the left adjoint of the Forgetful Functor from the category of Heyting algebras to that of Hilbert algebras. This Functor factorizes through the free implicative semilattice extension of a Hilbert algebra of Celani and Jansana [On the free implicative semilattice extension of a Hilbert algebra}. Mathematical Logic Quarterly 58, 3 (2012), 188--207].

T. M. G. Ahsanullah - One of the best experts on this subject based on the ideXlab platform.

  • On the category of fixed basis frame valued topological groups
    Fuzzy Sets and Systems, 2008
    Co-Authors: Jawaher Al-mufarrij, T. M. G. Ahsanullah
    Abstract:

    This article gives results on fixed basis frame valued neighborhood topological groups and stratified neighborhood topological groups, includes some characterization theorems, and presents the uniformizability of stratified neighborhood topological groups within the unified approach of Gutierrez Garcia, DePrada Vicente, and Sostak. It is shown that for a frame L, the category L-NGrp is topological over Grp with respect to the Forgetful Functor.