Closed categories, star-autonomy, and monoidal comonads
Craig Pastro, Ross Street
TL;DR
This paper investigates the conditions under which internal homs in a monoidal category can be lifted to its Eilenberg-Moore coalgebra category for a monoidal comonad, with applications to quantum groupoids.
Contribution
It characterizes the structure needed for lifting internal homs and applies this to reformulate the concept of quantum groupoid.
Findings
Identifies conditions for lifting internal homs in monoidal categories
Provides a framework for recasting quantum groupoid definitions
Enhances understanding of star-autonomy in monoidal categories
Abstract
This paper determines what structure is needed for internal homs in a monoidal category C to be liftable to the category C^G of Eilenberg-Moore coalgebras for a monoidal comonad G on C. We apply this to lift star-autonomy with the view to recasting the definition of quantum groupoid.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Topics in Algebra