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101.
David Pauksztello 《代数通讯》2013,41(2):386-394
The idea of a co-t-structure is almost ‘dual’ to that of a t-structure, but with some important differences. This note establishes co-t-structure analogues of Beligiannis and Reiten's corresponding results on compactly generated t-structures. 相似文献
102.
103.
Yu-Han Liu 《代数通讯》2013,41(8):3013-3031
We compute Balmer's prime spectrum for the derived category of quiver representations for a finite ordered quiver with the vertex-wise tensor product and show that it does not recover the quiver. We then associate an algebra to every k-linear triangulated tensor category and show that the path algebra can be recovered in this way. 相似文献
104.
Robert Lubarsky 《代数通讯》2013,41(4):1644-1649
Walker's cancellation theorem says that, if B ⊕ Z is isomorphic to C ⊕ Z in the category of abelian groups, then B is isomorphic to C. We construct an example in a diagram category of abelian groups where the theorem fails. As a consequence, the original theorem does not have a constructive proof even if B and C are subgroups of the free abelian group on two generators. Both of these results contrast with a group whose endomorphism ring has stable range one, which allows a constructive proof of cancellation and also a proof in any diagram category. 相似文献
105.
Semra Pamuk 《代数通讯》2013,41(7):3220-3243
Let G be a finite group and ? be a family of subgroups of G closed under conjugation and taking subgroups. We consider the question whether there exists a periodic relative ?-projective resolution for ? when ? is the family of all subgroups H ≤ G with rk H ≤ rkG ? 1. We answer this question negatively by calculating the relative group cohomology ?H*(G, 𝔽2) where G = ?/2 × ?/2 and ? is the family of cyclic subgroups of G. To do this calculation we first observe that the relative group cohomology ?H*(G, M) can be calculated using the ext-groups over the orbit category of G restricted to the family ?. In second part of the paper, we discuss the construction of a spectral sequence that converges to the cohomology of a group G and whose horizontal line at E 2 page is isomorphic to the relative group cohomology of G. 相似文献
106.
Cyclic posets are generalizations of cyclically ordered sets. In this article, we show that any cyclic poset gives rise to a Frobenius category over any discrete valuation ring R. The stable category of a Frobenius category is always triangulated and has a cluster structure in many cases. The continuous cluster categories of [14], the infinity-gon of [12], and the m-cluster category of type A ∞ (m ≥ 3) [13] are examples of this construction as well as some new examples such as the cluster category of ?2. An extension of this construction and further examples are given in [16]. 相似文献
107.
A subset systemZassigns to each partially ordered setPa certain collectionZ(P) of subsets. In this paper, a new kind of subset systems called directable subset systems is introduced. For a directable subset system Z, the concepts of F Z-way-below relation and F Z-domain are introduced. The well-known Scott topology is naturally generalized to the Z-level and the resulting topology is calledF Z-Scott topology, and the continuous functions with respect to this topology are characterized by preserving the suprema of directed Z-sets. Then, we mainly consider a generalization of the cartesian closedness of the categories DCPO of directed complete posets, BF of bifinite domains and FS ofF Sdomains to the Z-level. Corresponding to them, it is proved that, for a suitable subset system Z, the categories FZCPO ofZ-complete posets,FSFZ of finitely separated FZ-domains andBFFZ of bifiniteF Z-domains are all cartesian closed. Some examples of these categories are given. 相似文献
108.
We prove that, if F, G: 𝒞 → 𝒟 are two right exact functors between two Grothendieck categories such that they commute with coproducts and U is a generator of 𝒞, then there is a bijection between Nat(F, G) and the centralizer of Hom𝒟(F(U), G(U)) considered as an Hom𝒞(U, U)-Hom𝒞(U, U)-bimodule. We also prove a dual of this result and give applications to Frobenius functors between Grothendieck categories. 相似文献
109.
We introduce the concept of an object with the (finite) exchange property in an arbitrary Grothendieck category, and we present the basic properties of such an object. Applications are given for categories of graded modules and for categories of comodules over a coalgebra. Among other results, it is proved that an arbitrary coalgebra 𝒞 over a field has the finite exchange property. 相似文献
110.
In this article, we give necessary and sufficient conditions for a possibly nonassociative comodule algebra over a nonassociative Hopf algebra to have a total integral, thus extending the classical theory developed by Doi in the associative setting. Also, from this result we deduce a version of Maschke's Theorems and the consequent characterization of projectives for (H, B)-Hopf triples associated with a nonassociative Hopf algebra H and a nonassociative right H-comodule algebra B. 相似文献