BOHMANN, A.M. and SZYMIK, M. (2023) Boolean algebras, Morita invariance and the algebraic K-theory of Lawvere theories. Mathematical Proceedings of the Cambridge Philosophical Society, 175 (2). pp. 253-270. ISSN 0305-0041
Abstract
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.
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Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2023 The Authors. This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
Keywords: | 19D23: Symmetric monoidal categories; 06E05: Structure theory; 16D90: Module categories ; module theory in a category-theoretic context; Morita equivalence and duality; 18F25: Algebraic $K$-theory and $L$-theory; 18C10: Theories (e.g. algebraic theories), structure, and semantics; 55P42: Stable homotopy theory, spectra |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 26 Apr 2023 11:32 |
Last Modified: | 03 Oct 2024 13:55 |
Status: | Published |
Publisher: | Cambridge University Press (CUP) |
Refereed: | Yes |
Identification Number: | 10.1017/s0305004123000105 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:198554 |
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