8 papers · 1 filter
Intrinsic Geometry of Categorified Spectral Objects
Shih-Yu Chang
This paper develops the intrinsic geometry of the categorified spectral object associated with an admissible operator-semantic system in the Categorified S…
Categorified Spectral Duality: From Operator Systems to Spectral Stacks and Back
Shih-Yu Chang
Classical Gelfand duality provides an equivalence between commutative C-star algebras and topological spaces, but fails to furnish a geometric object for noncommutative operator sy…
A Universal Theory of Spectral Propagation for Compositional Operator Networks
Shih-Yu Chang
Classical spectral theory lacks a framework for understanding how spectra propagate through compositional systems like deep neural networks, feedback control loops, and quantum cir…
Spectral Operadic Calculus: Norm-Analytic Functor Calculus
Shih-Yu Chang
Classical spectral theory provides powerful tools for analyzing linear operators, but does not extend naturally to nonlinear or compositional settings. In particular, there is no g…
The Operadic Spectrum and Obstructions to Spectral Base Change
Shih-Yu Chang
We introduce an operadic notion of spectrum for algebras over colored operads in a symmetric monoidal category. The construction is defined via a canonical Hochschild-type object t…
Multicategorical Adjoints, Monadicity, and Quantum Resources
Shih-Yu Chang
This paper is the third part of a program aimed at building a unified operadic and multicategorical foundation for operator theory and quantum processes. Building on the multicateg…