2023/01/26 by Sarah Klanderman, Klanderman, Sarah, Maximilien Péroux +1 · 1 citation
Computer Science · #16T15 #18F30 #18M70 #18N10 #18N60 #19A99 #55P43 #55U15. Secondary: 16D90 #57T30 #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics #K-Theory and Homology (math.KT) #Primary: 16E40 #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2301.11346
openalex publication_date 2023/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.