let r be a commutative noetherian ring. we study the behavior of injectiveand at dimension of r-modules under the functors homr(-,-) and -×r-.

Given C-algebras A and B acting cyclically on Hilbert spaces H and K, respectively, we characterize completely isometric A, B-bimodule maps from B(K,H) into operator A, B-bimodules. We determine cogenerators in some classes of operator bimodules. For an injective cogenerator X in a suitable category of operator A, B-bimodules we show: if A, regarded as a Csubalgebra of Al(X) (adjointable left m...

This article extends results on regular implementablity in [3] and [8] to the case when the signal space is not an injective cogenerator, for instance, the space D of compactly supported smooth functions on R. In this case the bijective correspondence between behaviors and modules fails to hold; also projections and sums of behaviors need not in general be behaviors. A more general version of i...

For a locally presentable abelian category B with projective generator, we construct the derived and contraderived model structures on of complexes, proving in particular existence enough homotopy complexes objects. We also show that D(B) is generated, as triangulated coproducts, by generator B. Grothendieck A, injective coderived complexes. Assuming Vopěnka's principle, prove D(A) products, co...

Introduction Over the past several years there has been significant interest in adopting on-farm manure anaerobic digesters in Ontario. The potential for sustainable energy production, while reducing greenhouse gas (GHG) emissions, mitigating pathogens and odours, and increasing ionized nutrients in the digestate, has made anaerobic digestion an attractive option for manure management. The biog...

For a number of locally finitely presentable categories K we describe the codensity monad full embedding all objects into K. We introduce concept D-ultrafilter on an object, where D is “nice” cogenerator prove that assigns to every object representing D-ultrafilters it. Our result covers e.g. sets, vector spaces, posets, semilattices, graphs and M-sets for finite commutative monoids M.

Perturbations (r τt)t≥0 of the semigroup of shifts (τt)t≥0 on L(R+) are studied under the assumption that r τt−τt belongs to a certain Schatten–von Neumann class Sp with p ≥ 1. It is shown that, for the unitary component in the Wold– Kolmogorov decomposition of the cogenerator of the semigroup (r τt)t≥0, any singular spectral type may be achieved by S1-perturbations. An explicit construction is...