---
title: "Twisted Bicategorical Shadows and Traces"
authors:
  - "Zhonghui Sun"
year: 2026
venue: "arXiv:math.AT"
arxiv: "2609.04660"
doi: null
source: "https://arxiv.org/abs/2609.04660"
topics:
  - "curiosity"
  - "maths-foundations"
seed_rank: 1645
seed_batch: "curiosity-2026-09-09"
reviewed: "2026-09-09"
pool: "maths-foundations"
relevance_score: 10
lineage: bicategorical-traces
cites:
  - title: "Twisted Bicategorical Shadows and Traces"
    url: "https://arxiv.org/abs/2609.04660"
    year: 2026
    arxiv: "2609.04660"
    doi: null
see:
  - "1616-koszul-duality-and-morita-categories"
---

# Twisted Bicategorical Shadows and Traces

## One-sentence takeaway

Bicategorical shadows — the Morita-invariant home of Hochschild and THH — get a twisted upgrade that still carries traces.

## Why it's lovely

Why you might love this: shadows are the clean categorical reason Hochschild homology (and THH) is Morita-invariant, and the place where "trace" graduates from symmetric monoidal categories to bicategories. Twisting them equivariantly without breaking that story is spectator-sport category theory with immediate THH payoffs.

## Key ideas

- Bicategorical shadows unify HH / THH and encode Morita invariance.
- Traces extend from symmetric monoidal categories to bicategories via shadows.
- Twisted / equivariant variants that still support the shadow axioms.
- Connects to the Balmer / Morita / THH shelf already in the library.

## Caveats

Foundational/categorical; does not compute new THH of a specific ring spectrum. Read beside Morita / Koszul duality cards (1616) and THH-adjacent K-theory work.

## Links

- arXiv abs: https://arxiv.org/abs/2609.04660
- PDF: https://arxiv.org/pdf/2609.04660.pdf