THE FUNCTORS W AND Diag ◦Nerve ARE SIMPLICIALLY HOMOTOPY EQUIVALENT
نویسندگان
چکیده
Given a simplicial group G, there are two known classifying simplicial set constructions, the Kan classifying simplicial set WG and Diag NG, where N denotes the dimensionwise nerve. They are known to be weakly homotopy equivalent. We will show that WG is a strong simplicial deformation retract of Diag NG. In particular, WG and Diag NG are simplicially homotopy equivalent.
منابع مشابه
Function Complexes in Homotopical Algebra
1 .l Summary IN [l] QUILLEN introduced the notion of a model category (a category together with three classes of maps: weak equivalences, fibrations and cofibrations, satisfying certain axioms (1.4 (iv))) as a general framework for “doing homotopy theory”. To each model category M there is associated a homotopy category. If W C M denotes the subcategory of the weak equivalences, then this homot...
متن کاملSupporting information for: “Functional Mixed Effects Model for Small Area Estimation”
Y = ZF bF +Wν + Υ, where W = (ZR,M0, · · · ,Mp) and ν = (bR, U 0 , U 1 , · · · , U p ) . Denote G = var(ν) = diag(cov(bR), In ⊗ Σu0, · · · , In ⊗ Σup) and cov(Y ) = Σ. Also, Σi = Σi(δ) = ZFicov(bR)Z Fi + cov(Ui0) + ∑p k=1 Diag(Xik) cov(Uik)Diag(Xik) + Ωi for i = 1, . . . , n. The estimator of bF is b̂F = (Z T FΣ ZF ) −1ZT FΣ −1Y and the predictor of ν is ν̂ = GW TΣ−1(Y − ZF b̂F ). The covariance m...
متن کاملErratum: A General Waveguide Circuit Theory
Erratum: Equations D5 and E3 in the appendices of [1] contain typographical errors. They should read W ≡ diag(W í µí±); W í µí± ≡ í µí± � 0í µí± í µí±£ 0í µí± í µí± 0í µí± = í µí±£ 0í µí± * í µí±£ 0í µí± í µí± � 0í µí± í µí± 0í µí± * (D5) and U ≡ diag � |í µí±£ 0í µí± | í µí±£ 0í µí± �Re�í µí± ref í µí± � �í µí± ref í µí± � �. (E3) Also, the reference to Eq. (20) just after e...
متن کاملError Analysis of Qr Updating with Exponential Windowing
Exponential windowing is a widely used technique for suppressing the effects of old data as new data is added to a matrix. Specifically, given an n x p matrix Xn and a "forgetting factor" ß € (0, 1 ), one works with the matrix diag(/i'1_1, ß"~2, ... , \)Xn ■ In this paper we examine an updating algorithm for computing the QR factorization of diag(/j"-1, ß"~2 , ... , \)X„ and show that it is unc...
متن کاملAdaptive fuzzy terminal sliding mode control for a class of MIMO uncertain nonlinear systems
This paper presents a new adaptive terminal sliding mode tracking control design for a class of nonlinear systems using fuzzy logic system. The terminal sliding mode control (TSM) was developed to provide faster convergence and higher-precision control than the linear hyperplane-based sliding control. However, the original TSM encountered singularity problem with discontinuous control action. M...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008