Complete W*-categories

2024/11/03 by André Henriques, Nivedita Nivedita, Henriques, André +3 · 2 citations
Medicine · #Category Theory (math.CT) #FOS: Mathematics #Intracranial Aneurysms: Treatment and Complications #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2411.01678

openalex publication_date 2024/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study W^*-categories, and explain the ways in which complete W^*-categories behave like categorified Hilbert spaces. Every W^*-category C admits a canonical categorified inner product ⟨ , ⟩_Hilb : C× C → Hilb. Moreover, if C and D are complete W^*-categories there is an antilinear equivalence †:Func(C,D) ↔ Func(D,C) characterised by ⟨ c,F^†(d)⟩_Hilb ≃ ⟨ F(c),d⟩_Hilb, for c∈ C and d ∈ D.

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