We prove that the delooping, i. e., the classifying space, of a grouplike monoid is an H-space if and only if its multiplication is a homotopy homomorphism, extending and clarifying a result of Sugawara. Furthermore it is shown that the Moore loop space functor and the construction of the classifying space induce an adjunction of the according homotopy categories. 2000 Mathematics Subject Class...

historically, the majority of immigrants to the united states came from european countries. the 1965 immigration reform act (ira) fundamentally changed the configuration of immigrants to the united states. the largest immigrant communities now consist of latin americans, asians, and africans. another important development in immigrant communities in the past few decades has been the growth of a...

In the editorial, “A Crisis of Humanitarianism: Refugees at the Gates of Europe,” Marianna Fotaki elegantly highlights the changing dynamics of governmental policy toward refugees, forced migrants into Europe and the move away from the principles of humanitarianism.1 The perceived threats to economy, securi...

Let H be a cosemisimple Hopf algebra over an algebraically closed field. It is shown that if H has a simple subcoalgebra of dimension 9 and has no simple subcoalgebras of even dimension, then H contains either a grouplike element of order 2 or 3, or a family of simple subcoalgebras whose dimensions are the squares of each positive odd integer. In particular, if H is odd dimensional, then its di...

Let k be a commutative ring, A a k-algebra, C an A-coring that is projective as a left A-module, ∗C the dual ring of C and Λ a right C-comodule that is finitely generated as a left ∗C-module. We give necessary and sufficient conditions for projectivity and flatness of a module over the endomorphism ring EndC(Λ). If C contains a grouplike element, we can replace Λ with A.

Galois comodules over a coring can be characterised by properties of the relative injective comodules. They motivated the definition of Galois functors over some comonad (or monad) on any category and in the first section of the present paper we investigate the role of the relative injectives (projectives) in this context. Then we generalise the notion of corings (derived from an entwining of a...

The idea of “JSJ-decompositions” for 3-manifolds began with work of Waldhausen and was developed later through work of Jaco, Shalen and Johansen. It was shown that there is a finite collection of 2-sided, incompressible tori that separate a closed irreducible 3-manifold into pieces with strong topological structure. Sela introduced the idea of JSJ-decompositions for groups, an idea that has flo...

We generalize the notion of an anomaly for a symmetry to noninvertible enacted by surface operators using framework condensation in 2-categories. Given multifusion 2-category, potentially with some additional levels monoidality, we prove theorems about structure 2-category obtained condensing suitable algebra object. give examples where resulting category displays grouplike fusion rules and thr...