B. V. Novikov, L. Yu. Polyakova
The isomorphism of 0-homology groups of a categorical at zero semigroup and homology groups of its 0-reflector is proved. Some applications of 0-homology to Eilenberg-MacLane homology of semigroups are given.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Homology of higher categories
本文基于Eilenberg-Steenrod公理定义高阶范畴的同调，通过范畴论类比公理建立Dold-Kan对应，利用Street神经网络作为奇异复形，推导出具有乘法结构的高阶同调计算。
We use category-theoretic techniques to provide two proofs showing that for a higher-rank graph $Λ$, its cubical (co-)homology and categorical (co-)homology groups are isomorphic in all degrees, thus answering a question of Kumjian, Pask and Sims in the positive. Our first proof uses the topological realization of a higher-rank graph, which was introduced by Kaliszewski, Kumjian, Quigg, and Sims. In our more combinatorial second proof, we construct, explicitly and in both directions, maps on the level of (co-)chain complexes that implement said isomorphism. Along the way, we extend the definit…
Homology and twisted C*-algebras for self-similar actions and Zappa-Szép products
本文研究自相似作用对应的小范畴Zappa-Szép积的范畴同调，证明其可由双复形谱序列计算，并据此定义扭曲C*-代数并证明其基本结构性质。
We study the Hochschild homology of smooth spaces, emphasizing the importance of a pairing which generalizes Mukai's pairing on the cohomology of K3 surfaces. We show that integral transforms between derived categories of spaces induce, functorially, linear maps on homology. Adjoint functors induce adjoint linear maps with respect to the Mukai pairing. We define a Chern character with values in Hochschild homology, and we discuss analogues of the Hirzebruch-Riemann-Roch theorem and the Cardy Condition from physics. This is done in the context of a 2-category which has spaces as its objects and…
The theory of abelian categories proved very useful, providing an axiomatic framework for homology and cohomology of modules over a ring and, in particular, of abelian groups. For many years, a similar categorical framework has been lacking for non-abelian (co)homology, the subject of which includes the categories of non-abelian groups, of rings, Lie algebras, etc. The notion of semi-abelian category due to Janelidze, Marki and Tholen allows a unified study of many important homological properties of such categories. For instance, in any semi-abelian category, the classical diagram lemmas (the…
The subject of the present work is the de Rham part of non-commutative Hodge structures on the periodic cyclic homology of differential graded algebras and categories. We discuss explicit formulas for the corresponding connection on the periodic cyclic homology viewed as a bundle over the punctured formal disk. Our main result says that for the category of matrix factorizations of a polynomial the formulas reproduce, up to a certain shift, a well-known connection on the associated twisted de Rham cohomology which plays a central role in the geometric approach to the Hodge theory of isolated si…
Continuing our project on noncommutative (stable) homotopy we construct symmetric monoidal $\infty$-categorical models for separable $C^*$-algebras $\mathtt{SC^*_\infty}$ and noncommutative spectra $\mathtt{NSp}$ using the framework of Higher Algebra due to Lurie. We study smashing (co)localizations of $\mathtt{SC^*_\infty}$ and $\mathtt{NSp}$ with respect to strongly self-absorbing $C^*$-algebras. We analyse the homotopy categories of the localizations of $\mathtt{SC^*_\infty}$ and give universal characterizations thereof. We construct a stable $\infty$-categorical model for bivariant connect…
Galois theory and homology in quasi-abelian functor categories
本文研究有限范畴T上的函子范畴[T,A]（A为拟阿贝尔范畴），定义并证明其子范畴F为无挠Birkhoff子范畴，从而用于研究中心扩张和同调的广义Hopf公式。
Isomorphisms in K-theory from isomorphisms in groupoid homology theories
该研究证明无挠顺从充裕群胚中由平展对应诱导的群胚同调同构可导出相关$\text{C}^\text{*}$-代数K-理论同构，借此推广了X. Li的左正则逆半群$\text{C}^\text{*}$-代数K-理论公式，核心方法是发展ABC谱序列的函子性。
Finite group actions on dg categories and Hochschild homology
研究微分分次范畴上有限群作用的等变微分分次范畴的霍赫希尔德同调群分解，揭示基域特定时该分解与范畴作用、表示环作用的关联。
In all known explicit computations on Weinstein manifolds, the self-wrapped Floer homology of non-compact exact Lagrangian is always either infinite-dimensional or zero. We show that a global variant of this observed phenomenon holds in broad generality: the wrapped Fukaya category of any positive-dimensional Weinstein (or non-degenerate Liouville) manifold is always either non-proper or zero, as is any quotient thereof. Moreover any non-compact connected exact Lagrangian is always either a "(both left and right) non-proper object" or zero in such a wrapped Fukaya category, as is any idempoten…
Chern character for torsion-free ample groupoids
本文构建了从 Baum-Connes 组合映射域到 Crainic-Moerdijk 群oids 带有有理系数的同调群的 Chern 符号映射，验证了 Matui 的 HK 猜想变体，并应用于超几何动力系统、拓扑满群同调等。
Rigidity, Generators and Homology of Interval Exchange Groups
本文通过构造部分变换群胚将区间交换群实现为拓扑全群，证明其群胚同调与子群同调的关系及C*-代数可分类性，并给出三类关键情形的同调计算与显式生成元。
We compute the stable homology of orthogonal and symplectic groups over a finite field k with coefficients coming from an usual endofunctor F of k-vector spaces (exterior, symmetric, divided powers...), that is, for all natural integer i, we compute the colimits of the vector spaces $H_i(O_{n,n}(k) ; F(k^{2n}))$ and $H_i(Sp_{2n}(k) ; F(k^{2n}))$. In this situation, the stabilization is a classical result of Charney. We give a formal framework to connect stable homology of some families of groups and homology of suitable small categories thanks to a spectral sequence which collapses in several …
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。