2022/04/24 by Chirvasitu, Alexandru
#18A30 #18A40 #18C20 #18C35 #43A22 #46L05 #46L52 #46L67 #Category Theory (math.CT) #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.2204.11319
We prove that an action ρ:A→ M(C0(\mathbbG)⊗ A) of a locally compact quantum group on a C^*-algebra has a universal equivariant compactification, and prove a number of other category-theoretic results on \mathbbG-equivariant compactifications: that the categories compactifications of ρ and A respectively are locally presentable (hence complete and cocomplete), that the forgetful functor between them is a colimit-creating left adjoint, and that epimorphisms therein are surjective and injections are regular monomorphisms. When \mathbbG is regular coamenable we also show that the forgetful functor from unital \mathbbG-C^*-algebras to unital C^*-algebras creates finite limits and is comonadic, and that the monomorphisms in the former category are injective.