On topological coHochschild homology and cotensor products

2025/05/20 by Zha, Jiaxi
#Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.14474

Abstract

In this work, we first study the cotensor product of comodules in the ∞-category Mod_R for a connected 𝔼_∞-ring spectrum R. We then apply these results to analyze higher coalgebra structures of topological coHochschild homology (coTHH) and establish its Morita-Takeuchi invariance, which are precisely dual to the corresponding properties of topological Hochschild homology.

Citations

• Trace methods for coHochschild homology
• Characters and transfer maps via categorified traces
• Integral topological Hochschild homology of connective complex K-theory
• Computations of relative topological coHochschild homology
• Topological coHochschild Homology and the Homology of Free Loop Spaces
• Spanier-Whitehead duality for topological coHochschild homology
• Redshift and multiplication for truncated Brown-Peterson spectra
• The coalgebraic enrichment of algebras in higher categories
• Topological cyclic homology
• Invariance properties of coHochschild homology
• Coalgebras in symmetric monoidal categories of spectra
• Higher traces, noncommutative motives, and the categorified Chern character
• Dualizing cartesian and cocartesian fibrations
• Waldhausen K-theory of spaces via comodules
• Topological Hochschild homology of l and ko
• Higher Topos Theory

Related

• Invariance properties of coHochschild homology
• Computations of relative topological coHochschild homology
• Spanier-Whitehead duality for topological coHochschild homology
• Cotensor products of modules
• On Bialgebras, Comodules, Descent Data and Thom Spectra in ∞-categories