Generalizations of Loday’s assembly maps for Lawvere’s algebraic theories
Peer reviewed, Journal article
Published version
Permanent lenke
https://hdl.handle.net/11250/3109667Utgivelsesdato
2023Metadata
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- Institutt for matematiske fag [2531]
- Publikasjoner fra CRIStin - NTNU [38672]
Originalversjon
10.1017/S1474748022000603Sammendrag
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 generalisation 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 nonabelian interpolation scheme, raising novel questions. Numerous examples illustrate the scope of our extension.