Comonad cohomology of track categories

IF 0.7 4区数学 Q2 MATHEMATICS Journal of Homotopy and Related Structures Pub Date : 2019-05-14 DOI:10.1007/s40062-019-00235-2

David Blanc, Simona Paoli

引用次数: 1

Abstract

We define a comonad cohomology of track categories, and show that it is related via a long exact sequence to the corresponding \(({\mathcal {S}}\!,\!\mathcal {O})\)-cohomology. Under mild hypotheses, the comonad cohomology coincides, up to reindexing, with the \(({\mathcal {S}}\!,\!\mathcal {O})\)-cohomology, yielding an algebraic description of the latter. We also specialize to the case where the track category is a 2-groupoid.

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轨道范畴的共上同调

我们定义了轨迹范畴的共上同调，并证明了它通过一个长精确序列与对应的\(({\mathcal {S}}\!,\!\mathcal {O})\) -上同调相关。在温和的假设下，共上同调与\(({\mathcal {S}}\!,\!\mathcal {O})\) -上同调重合，直至重合，产生了后者的代数描述。我们还专门研究轨道类别是2-groupoid的情况。

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来源期刊

Journal of Homotopy and Related Structures MATHEMATICS-

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences. Journal of Homotopy and Related Structures is intended to publish papers on Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.

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