Frobenius Objects in Cartesian Bicategories
R. F. C. Walters, R. J. Wood
TL;DR
This paper explores the properties of Frobenius objects within cartesian bicategories, revealing that maps between them are exactly comonoid homomorphisms and that certain hom-categories form groupoids.
Contribution
It characterizes the nature of maps between Frobenius objects and shows the groupoid structure of hom-categories in this context.
Findings
Maps between Frobenius objects are comonoid homomorphisms
Hom-categories from any object to a Frobenius object form groupoids
Provides a categorical framework for Frobenius objects in bicategories
Abstract
Maps (left adjoint arrows) between Frobenius objects in a cartesian bicategory B are precisely comonoid homomorphisms and, for A Frobenius and any T in B, map(B)(T,A) is a groupoid.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Topics in Algebra