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arXiv · 2301.11346

Trace methods for coHochschild homology

Sarah Klanderman·Maximilien Péroux
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Abstract

Hochschild homology is a classical invariant of rings that plays an important role because of its connection to algebraic $K$-theory via the Dennis trace. At level zero, the Dennis trace is induced by the Hattori-Stallings trace. In this paper, we introduce new algebraic $K$-theories of coalgebras and obtain coalgebraic refinements of the Hattori-Stallings trace that connect these algebraic $K$-theories to coHochschild homology (the invariant analogous to Hochschild homology but for coalgebras). We employ bicategorical methods of Ponto to show that coHochschild homology is a shadow. Consequently, we obtain that coHochschild homology is Morita-Takeuchi invariant.

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Sarah Klanderman, Maximilien Péroux. 2023-01-26. Trace methods for coHochschild homology. https://arxiv.org/abs/2301.11346

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