By recent results in [19], the standard localization theory for function and section spaces due to Hilton-Mislin-Roitberg and Möller extend outside the CW category to the case of compact metric domain in the presence of a grouplike structure. We study applications in two cases directly generalizing the gauge group of a principal bundle. We prove an identity for the monoid aut(ξ) of fibre-homoto...

We define an “algebraic” version of the Goodwillie tower, P alg n F (X), that depends only on the behavior of F on coproducts of X . When F is a functor to connected spaces or grouplike H-spaces, the functor P alg n F is the base of a fibration |⊥ F | → F → P alg n F, whose fiber is the simplicial space associated to a cotriple ⊥ built from the (n + 1) cross effect of the functor F . When the c...

Let i : A → R be a ring morphism, and χ : R → A a right R-linear map with χ(χ(r)s) = χ(rs) and χ(1 R) = 1 A. If R is a Frobenius A-ring, then we can define a trace map tr : A → A R. If there exists an element of trace 1 in A, then A is right FBN if and only if A R is right FBN and A is right noetherian. The result can be generalized to the case where R is an I-Frobenius A-ring, and the conditio...

Let i : A → R be a ring morphism, and χ : R → A a right R-linear map with χ(χ(r)s) = χ(rs) and χ(1 R) = 1 A. If R is a Frobenius A-ring, then we can define a trace map tr : A → A R. If there exists an element of trace 1 in A, then A is right FBN if and only if A R is right FBN and A is right noetherian. The result can be generalized to the case where R is an I-Frobenius A-ring. We recover resul...

the cycle of protests that swept the united states beginning in 2010 has its roots in the growing disillusionment of a significant portion of the american populace in the prospects and opportunities for growth and development. despite the extensive myopia of various sectors of the american public vis a vis the rest of the world, if there is one thing much of the american public holds dear is th...

In his article Class in American Legal Education, Professor Richard Sander highlights the lack of class diversity within law schools in the United States, particularly within elite law schools. As Sander points out, law students tend to come from relatively elite class backgrounds, and Sander urges law schools to pursue class-based affirmative action, rather than race-based affirmative action, ...