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arXiv 2011.11755math.KTmath.AT
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布尔代数、Morita 不变性与 Lawvere 理论的代数 K-理论

Boolean algebras, Morita invariance, and the algebraic K-theory of Lawvere theories

Anna Marie Bohmann, Markus Szymik

备注：
22 pages. This updated paper discusses the work on Morita equivalence of Lawvere theories that appeared in version one. In order to better highlight the two separate directions of the results in that first version, the material on assembly maps has been incorporated into a second paper, arXiv:2112.07003. Revised version; to appear in Math. Proc. Cambridge Philos. Soc
发表信息：
Math. Proc. Camb. Phil. Soc. 175 (2023) 253-270
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AI总结：

本文研究了 Lawvere 理论的 Morita 等价类与代数 K-理论的相互作用，证明了高阶代数 K-理论在矩阵理论下不变，但因非加性上下文中幂等元行为而不具备完全 Morita 不变性，并计算了与布尔代数理论等价的所有理论的 K-理论。

摘要：

Lawvere 理论的代数 K-理论是一种概念性工具，用于阐明代数结构（如置换群和自由群的自同构群）的对称群的同调。本文全面探讨了 Lawvere 理论的 Morita 等价类如何与代数 K-理论相互作用。一方面，我们证明了高阶代数 K-理论在过渡到矩阵理论时是不变的。另一方面，由于非加性上下文中幂等元的行为，我们证明了高阶代数 K-理论并不具有完全的 Morita 不变性：我们计算了所有与布尔代数理论 Morita 等价的 Lawvere 理论的 K-理论。

英文摘要：

The algebraic K-theory of Lawvere theories is a conceptual device to elucidate the stable homology of the symmetry groups of algebraic structures such as the permutation groups and the automorphism groups of free groups. In this paper, we fully address the question of how Morita equivalence classes of Lawvere theories interact with algebraic K-theory. On the one hand, we show that the higher algebraic K-theory is invariant under passage to matrix theories. On the other hand, we show that the higher algebraic K-theory is not fully Morita invariant because of the behavior of idempotents in non-additive contexts: We compute the K-theory of all Lawvere theories Morita equivalent to the theory of Boolean algebras.

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。

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