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For any ring we propose the construction of a cover which increases the finitistic dimension on one side and decreases the finitistic dimension to zero on the opposite side. This complements recent work of Cummings.

Given a tilting object of the derived category of an abelian category of finite global dimension, we give (under suitable finiteness conditions) a bound for the global dimension of its endomorphism ring.

For any essentially small triangulated category, the centre of its lattice of thick subcategories is introduced; it is a spatial frame and yields a notion of central support. A relative version of this centre recovers the support theory for tensor triangulated categories and provides a universal notion of cohomological support. Along the way, we establish Mayer–Vietoris sequences for pairs of commuting subcategories. [ABSTRACT FROM AUTHOR]

For a tensor‐triangulated category and any regular cardinal α$\alpha$, we study the frame of α$\alpha$‐localizing tensor ideals and its associated space of points. For a well‐generated category and its frame of localizing tensor ideals, we provide conditions such that the associated space is obtained by refining the topology of the corresponding space for the triangulated subcategory of α$\alpha$‐compact objects. This is illustrated by several known examples for α=ℵ0$\alpha =\aleph _0$, and new spaces arise for α>ℵ0$\alpha >\aleph _0$. [ABSTRACT FROM AUTHOR]

We develop a support theory for elementary supergroup schemes, over a field of positive characteristic p ≥ 3, starting with a definition of a π-point generalising cyclic shifted subgroups of Carlson for elementary abelian groups and π-points of Friedlander and Pevtsova for finite group schemes. These are defined in terms of maps from the graded algebra k[t,τ]/(tp−τ2), where t has even degree and τ has odd degree. The strength of the theory is demonstrated by classifying the parity change invariant localising subcategories of the stable module category of an elementary supergroup scheme. [ABSTRACT FROM AUTHOR]

We prove that every flat tensor-idempotent in the module category Mod-Tc of a tensor-triangulated category comes from a unique smashing ideal in. We deduce that the lattice of smashing ideals forms a frame. [ABSTRACT FROM AUTHOR]

Auslander-Reiten duality for module categories is generalised to Grothendieck abelian categories that have a sufficient supply of finitely presented objects. It is shown that Auslander-Reiten duality amounts to the fact that the functor Ext¹(C,−) into modules over the endomorphism ring of C admits a partially defined right adjoint when C is a finitely presented object. This result seems to be new even for module categories. For appropriate schemes over a field, the connection with Serre duality is discussed. [ABSTRACT FROM AUTHOR]

A duality theorem for the stable module category of representations of a finite group scheme is proved. One of its consequences is an analogue of Serre duality, and the existence of Auslander–Reiten triangles for the p-local and p-torsion subcategories of the stable category, for each homogeneous prime ideal p in the cohomology ring of the group scheme. [ABSTRACT FROM AUTHOR]

African indigenous vegetables (AIVs) have high nutritional value, forming a potent weapon against the pressing hidden hunger problem in East Africa, but they are not sufficiently adopted as cash crops by Kenyan small-scale farmers to meet the rising demand in the urban areas. This study therefore aims (i) to explore which factors motivate small-scale farmers to specialize in commercial AIV production and (ii) to assess the impact of AIV production on household income and food security. This analysis was based on primary data from 706 rural and peri-urban small-scale vegetable producers in Kenya. Results of a binary choice model showed that education, participation in producer groups, access to market information and irrigation water, as well as distance to the next city influenced the decision to commercialize AIV production. Impact analysis was conducted with binary and continuous propensity score matching (PSM) and endogenous switching regression (ESR). The production of AIVs as cash crops positively influenced the total per capita household income and the food security status of the households. [ABSTRACT FROM AUTHOR]

A set valued representation of the Kronecker quiver is nothing but a quiver. We apply the forgetful functor from vector spaces to sets and compare linear with set valued representations of the Kronecker quiver. [ABSTRACT FROM PUBLISHER]

We introduce the notion of $$\pi $$ -cosupport as a new tool for the stable module category of a finite group scheme. In the case of a finite group, we use this to give a new proof of the classification of tensor ideal localising subcategories. In a sequel to this paper, we carry out the corresponding classification for finite group schemes. [ABSTRACT FROM AUTHOR]

We present a categorification of the non-crossing partitions given by crystallographic Coxeter groups. This involves a category of certain bilinear lattices, which are essentially determined by a symmetrisable generalised Cartan matrix together with a particular choice of a Coxeter element. Examples arise from Grothendieck groups of hereditary artin algebras. [ABSTRACT FROM AUTHOR]

We describe a procedure for constructing morphisms in additive categories, combining Auslander's concept of a morphism determined by an object with the existence of flat covers. Also, we show how flat covers are turned into projective covers and we interpret these constructions in terms of adjoint functors. [ABSTRACT FROM AUTHOR]

Polynomial representations of general linear groups and modules over Schur algebras are compared. We work over an arbitrary commutative ring and show that Schur-Weyl duality is the key for an equivalence between both categories. [ABSTRACT FROM AUTHOR]

We compute the Krull–Gabriel dimension of the category of perfect complexes for finite dimensional algebras which are derived discrete. [ABSTRACT FROM AUTHOR]

Local cohomology functors are constructed for the category of cohomological functors on an essentially small triangulated category ⊺ equipped with an action of a commutative noetherian ring. This is used to establish a local-global principle and to develop a notion of stratification, for ⊺ and the cohomological functors on it, analogous to such concepts for compactly generated triangulated categories. [ABSTRACT FROM AUTHOR]

We discuss the notion of strongly unbounded type for abelian length categories; this is closely related to the Second Brauer–Thrall Conjecture for Artin algebras. A new ingredient is the space of characters in the sense of Crawley-Boevey. [ABSTRACT FROM AUTHOR]

Inclusion-preserving maps from modules over an Artin algebra to complete partially ordered sets are studied. This yields a filtration of the Ziegler spectrum that is indexed by all Gabriel–Roiter measures. Another application is a compactness result for the set of subcategories of finitely presented modules that are closed under submodules. [ABSTRACT FROM AUTHOR]

This is a report on recent work of Chałupnik and Touzé. We explain the Koszul duality for the category of strict polynomial functors and make explicit the underlying monoidal structure which seems to be of independent interest. Then we connect this to Ringel duality for Schur algebras and describe Serre duality for strict polynomial functors. [ABSTRACT FROM PUBLISHER]

The Hom closed colocalizing subcategories of the stable module category of a finite group are classified. Along the way, the colocalizing subcategories of the homotopy category of injectives over an exterior algebra, and the derived category of a formal commutative differential graded algebra, are classified. To this end, and with an eye towards future applications, a notion of local homology and cosupport for triangulated categories is developed, building on earlier work of the authors on local cohomology and support. [ABSTRACT FROM AUTHOR]