Levelwise modules over separable monads on stable derivators
Ioannis Lagkas-Nikolos
TL;DR
This paper demonstrates that for a separable cocontinuous monad on a stable derivator, the module categories form a stable derivator, and provides examples of derivators satisfying most stability axioms without the strongness condition.
Contribution
It establishes a method to glue levelwise Eilenberg-Moore categories into a stable derivator and offers new examples of derivators nearly satisfying all stability axioms.
Findings
Levelwise Eilenberg-Moore categories form a stable derivator.
Examples of derivators satisfying all but the strongness axiom.
Application of separable cocontinuous monads in derivator theory.
Abstract
We show that given a separable cocontinuous monad on a stable derivator, the levelwise Eilenberg-Moore categories of modules glue together to a stable derivator. As an application, we give examples of derivators that satisfy all the axioms for stability except the strongness one.
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