An operadic spectrum acts as a control parameter for a norm-analytic functor calculus, delivering criteria for polynomial behavior, exponential convergence bounds on Taylor towers, and a reconstruction theorem from derivative data via operadic plethysm.
Weibel,An Introduction to Homological Algebra, Cambridge University Press, 1994
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Asymptotic universal Koszulity is defined for graded algebras and shown to hold for Galois cohomology rings of pro-p groups via colimit theorems from finite quotients.
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Spectral Operadic Calculus: Norm-Analytic Functor Calculus
An operadic spectrum acts as a control parameter for a norm-analytic functor calculus, delivering criteria for polynomial behavior, exponential convergence bounds on Taylor towers, and a reconstruction theorem from derivative data via operadic plethysm.
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Asymptotic Universal Koszulity in Galois Cohomology
Asymptotic universal Koszulity is defined for graded algebras and shown to hold for Galois cohomology rings of pro-p groups via colimit theorems from finite quotients.