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The paper is devoted to a kind of "very non-abelian" spectral categories. Under strong conditions on a category X, we prove, among other things, that, for a given faithful localization C→X, we have canonical equivalences Spec(C)∼X∼(category of injective objects in C), and that C has natural injective envelopes. [ABSTRACT FROM AUTHOR]

We introduce and investigate weak relative Rickart objects and dual weak relative Rickart objects in abelian categories. Several types of abelian categories are characterized in terms of (dual) weak relative Rickart properties. We relate our theory to the study of relative regular objects and (dual) relative Baer objects. We also give some applications to module and comodule categories. [ABSTRACT FROM AUTHOR]

We introduce and study relative Rickart objects and dual relative Rickart objects in abelian categories. We show how our theory may be employed in order to study relative regular objects and (dual) relative Baer objects in abelian categories. We also give applications to module and comodule categories. [ABSTRACT FROM AUTHOR]

In compliance with the Quality Assurance Framework for Earth Observation (QA4EO) guidelines, the goal of this paper is to provide a theoretical comparison and an experimental quality assessment of two operational (ready-for-use) expert systems (prior knowledge-based nonadaptive decision trees) for automatic near real-time preattentional classification and segmentation of spaceborne/airborne multispectral (MS) images: the Satellite Image Automatic Mapper™ (SIAM™) software product and the Spectral Classification of surface reflectance signatures (SPECL) secondary product of the Atmospheric/Topographic Correction™ (ATCOR™) commercial software toolbox. For the sake of simplicity, this paper is split into two: Part 1—Theory, presented herein, and Part 2—Experimental results, already published elsewhere. The main theoretical contribution of the present Part 1 is threefold. First, it provides the published Part 2 with an interdisciplinary terminology and a theoretical background encompassing multiple disciplines, such as philosophical hermeneutics, machine learning, artificial intelligence, computer vision, human vision, and remote sensing (RS). Second, it highlights the several degrees of novelty of the ATCOR-SPECL and SIAM deductive preliminary classifiers (preclassifiers) at the four levels of abstraction of an information processing system, namely, system design, knowledge/information representation, algorithms, and implementation. Third, the present Part 1 requires the experimental Part 2 to collect a minimum set of complementary statistically independent metrological quality indicators (QIs) of operativeness (QIOs), in compliance with the QA4EO guidelines and the principles of statistics. In particular, sample QIs are required to be: 1) statistically significant, i.e., provided with a degree of uncertainty in measurement; and 2) statistically valid (consistent), i.e., representative of the entire population being sampled, which requires the implementation of a probability sampling protocol. Largely overlooked by the RS community, these sample QI requirements are almost never satisfied in the RS common practice. As a consequence, to date, QIOs of existing RS image understanding systems (RS-IUSs), including thematic map accuracy, remain largely unknown in statistical terms. The conclusion of the present Part 1 is that the proposed comparison of the two alternative ATCOR-SPECL and SIAM prior knowledge-based preclassifiers in operating mode, accomplished in the Part 2, can be considered appropriate, well-timed, and of potential interest to a large portion of the RS readership. [ABSTRACT FROM PUBLISHER]

A kind of motivic algebra of spectral categories and modules over them is developed to introduce K-motives of algebraic varieties. As an application, bivariant algebraic K-theory K(X; Y) as well as bivariant motivic cohomology groups Hp,q(X; Y;ℤ) are defined and studied. We use Grayson's machinery [12] to produce the Grayson motivic spectral sequence connecting bivariant K-theory to bivariant motivic cohomology. It is shown that the spectral sequence is naturally realized in the triangulated category of K-motives constructed in the paper. It is also shown that ordinary algebraic K-theory is represented by the K-motive of the point. [ABSTRACT FROM AUTHOR]

Abstract: We construct a Quillen model structure on the category of spectral categories, where the weak equivalences are the symmetric spectra analogue of the notion of equivalence of categories. [Copyright &y& Elsevier]

Abstract: A Grothendieck category is said to be locally finitely generated if the subobject lattice of every object in is compactly generated, or equivalently, if possesses a family of finitely generated generators. Every nonzero locally finitely generated Grothendieck category possesses simple objects. We shall call a Grothendieck category indecomposable if is not equivalent to a product of nonzero Grothendieck categories . In this paper an example of an indecomposable nonlocally finitely generated Grothendieck category possessing simple objects is constructed, answering in the negative a sharper form of a question posed by Albu, Iosif, and Teply in [T. Albu, M. Iosif, M.L. Teply, Dual Krull dimension and quotient finite dimensionality, J. Algebra 284 (2005) 52–79]. [Copyright &y& Elsevier]