2025/06/03 by Winges, Christoph, Christoph Winges, Nielsen, Marius · 1 citation
Computer Science · #Constraint Satisfaction and Optimization
paper · pdf · doi:10.48550/arxiv.2506.02598
We prove an analogue of the Gabriel--Quillen embedding theorem for exact ∞-categories, giving rise to a presentable version of Klemenc's stable envelope of an exact ∞-category. Moreover, we construct a symmetric monoidal structure on the ∞-category of small exact ∞-categories and discuss the multiplicative properties of the Gabriel--Quillen embedding. For E an Adams-type homotopy associative ring spectrum, this allows us to identify the symmetric monoidal ∞-category of E-based synthetic spectra with the presentable stable envelope of the exact ∞-category of compact spectra with finite projective E-homology. In addition, we show that algebraic K-theory, considered as a functor on exact ∞-categories, admits a unique delooping as a localising invariant.