Let R be a commutative Noetherian ring and let G be the category of modules of G-dimension zero over R. We denote the associated stable category by G. We show that the functor category modG is a Frobenius category and we argue how this property could characterize G as a subcategory of modR.

Let S be a site. We introduce the notion of extension of strictly commutative Picard S-stacks. Applying this notion to 1-motives, we get the notion of extension of 1-motives and we prove the following conjecture of Deligne: if MRZ(k) denotes the integral version of the neutral Tannakian category of mixed realizations over an algebraically closed field k, then the subcategory of MRZ(k) generated...

Let X be an algebraic variety over a base scheme S and φ : T → S a faithful base change. Given an admissible subcategory A in D(X), the bounded derived category of coherent sheaves on X, we construct an admissible subcategory AT in D b(X×ST ), called the base change of A, in such a way that the following base change theorem holds: if a semiorthogonal decomposition of D(X) is given then the base...

We classify the “quotients” of a tannakian category in which the objects of a tannakian subcategory become trivial, and we examine the properties of such quotient categories.

Extriangulated categories were introduced by Nakaoka and Palu to give a unification of properties in exact triangulated categories. We consider this article the Grothendieck group K0(C) an extriangulated category C. show that locally finite C always has almost split extensions case relations are generated Auslander-Rieten E-triangles. partial converse result when restricting with cluster tiltin...

The Diagnostic and Statistical Manual of Mental Disorders has included three subgroups of pedophilic disorder based on the gender of the victim, the exclusiveness of the subject's preference for children, and whether the behavior is limited to incest. This study uses the pedophile's preference for age of victim as a means of delineating two distinct subgroups. The first group of so-called 'infa...

In this paper we show that there is no left adjoint to the inclusion functor from the full subcategory C 0 of Scott domains (i.e., consistently complete ! algebraic cpo's) to SFP, the category of SFP-objects and Scott-continuous maps. We also show there is no left adjoint to the inclusion functor from C 0 to any larger category of cpo's which contains a simple ve-element domain. As a corollary,...

The oil from the 2010 Deepwater Horizon spill in the Gulf of Mexico was documented by shoreline assessment teams as stranding on 1,773 km of shoreline. Beaches comprised 50.8%, marshes 44.9%, and other shoreline types 4.3% of the oiled shoreline. Shoreline cleanup activities were authorized on 660 km, or 73.3% of oiled beaches and up to 71 km, or 8.9% of oiled marshes and associated habitats. O...

The homotopy category of complexes of projective left-modules over any reasonably nice ring is proved to be a compactly generated triangulated category, and a duality is given between its subcategory of compact objects and the finite derived category of right-modules.

We exhibit a triangulated category which is neither the stable category of a Frobenius category nor a full triangulated subcategory of the homotopy category of a stable model category.