论文标题
晶格和塔斯基laplacian的蜂窝滑轮
Cellular Sheaves of Lattices and the Tarski Laplacian
论文作者
论文摘要
本文启动了一个离散的霍奇理论，用于在晶格和galois连接类别中采用值。关键的发展是塔斯基·拉普拉斯（Tarski Laplacian），这是对科班综合体的内态性，其固定点产生了同时与全球部分函数符合度为零的同事。这在网络和更广泛的潜在应用程序上的共识和分布优化问题中立即应用。
This paper initiates a discrete Hodge theory for cellular sheaves taking values in a category of lattices and Galois connections. The key development is the Tarski Laplacian, an endomorphism on the cochain complex whose fixed points yield a cohomology that agrees with the global section functor in degree zero. This has immediate applications in consensus and distributed optimization problems over networks and broader potential applications.
