arXiv Open Access 2021

Generalizations of Loday's assembly maps for Lawvere's algebraic theories

Anna Marie Bohmann Markus Szymik

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Abstrak

Loday's assembly maps approximate the K-theory of group rings by the K-theory of the coefficient ring and the corresponding homology of the group. We present a generalization that places both ingredients on the same footing. Building on Elmendorf--Mandell's multiplicativity results and our earlier work, we show that the K-theory of Lawvere theories is lax monoidal. This result makes it possible to present our theory in a user-friendly way without using higher categorical language. It also allows us to extend the idea to new contexts and set up a non-abelian interpolation scheme, raising novel questions. Numerous examples illustrate the scope of our extension.

Topik & Kata Kunci

math.KT math.AT

Penulis (2)

Anna Marie Bohmann

Markus Szymik

Format Sitasi

APA MLA BibTeX

Bohmann, A.M., Szymik, M. (2021). Generalizations of Loday's assembly maps for Lawvere's algebraic theories. https://arxiv.org/abs/2112.07003

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Informasi Jurnal

Tahun Terbit: 2021
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓