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Braided categorical groups and strictifying associators
Homology, Homotopy and Applications ( IF 0.5 ) Pub Date : 2020-01-01 , DOI: 10.4310/hha.2020.v22.n2.a19 Oliver Braunling 1
Homology, Homotopy and Applications ( IF 0.5 ) Pub Date : 2020-01-01 , DOI: 10.4310/hha.2020.v22.n2.a19 Oliver Braunling 1
Affiliation
A key invariant of a braided categorical group is its quadratic form, introduced by Joyal and Street. We show that the categorical group is braided equivalent to a simultaneously skeletal and strictly associative one if and only if the polarization of this quadratic form is the symmetrization of a bilinear form. This generalizes the result of Johnson-Osorno that all Picard groupoids can simultaneously be strictified and skeletalized, except that in the braided case there is a genuine obstruction.
中文翻译:
编织分类组和严格关联者
编织分类群的一个关键不变量是它的二次形式,由 Joyal 和 Street 引入。我们表明,当且仅当这种二次形式的极化是双线性形式的对称化时,分类群被编织等价于同时具有骨架和严格结合的群。这概括了 Johnson-Osorno 的结果,即所有 Picard groupoids 可以同时被严格化和骨架化,除了在编织情况下存在真正的阻塞。
更新日期:2020-01-01
中文翻译:
编织分类组和严格关联者
编织分类群的一个关键不变量是它的二次形式,由 Joyal 和 Street 引入。我们表明,当且仅当这种二次形式的极化是双线性形式的对称化时,分类群被编织等价于同时具有骨架和严格结合的群。这概括了 Johnson-Osorno 的结果,即所有 Picard groupoids 可以同时被严格化和骨架化,除了在编织情况下存在真正的阻塞。