ar X iv : m at h / 06 06 47 2 v 1 [ m at h . C T ] 1 9 Ju n 20 06 Generalized 2 - vector spaces and general linear 2 - groups Josep
نویسنده
چکیده
In this paper a notion of generalized 2-vector space is introduced which includes Kapranov and Voevodsky 2-vector spaces. Various kinds of generalized 2-vector spaces are considered and examples are given. The existence of non free generalized 2-vector spaces and of generalized 2-vector spaces which are non Karoubian (hence, non abelian) categories is discussed, and it is shown how any generalized 2-vector space can be identified with a full subcategory of an (abelian) functor category with values in the category VECTK of (possibly infinite dimensional) vector spaces. The corresponding general linear 2-groups GL(VectK [C]) are considered. Specifically, it is shown that GL(VectK [C]) always contains as a (non full) sub-2-group the 2-group EquivCat(C) (hence, for finite categories C, they contain Weyl sub-2-groups analogous to the usual Weyl subgroups of the general linear groups), and GL(VectK [C]) is explicitly computed (up to equivalence) in a special case of generalized 2-vector spaces which include those of Kapranov and Voevodsky. Finally, other important drawbacks of the notion of generalized 2-vector space, besides the fact that it is in general a non Karoubian category, are also mentioned at the end of the paper.
منابع مشابه
ar X iv : m at h / 06 06 67 1 v 1 [ m at h . A C ] 2 7 Ju n 20 06 PRÜFER ⋆ – MULTIPLICATION DOMAINS AND ⋆ – COHERENCE
متن کامل
ar X iv : m at h / 06 06 33 9 v 1 [ m at h . SP ] 1 4 Ju n 20 06 Eigenfunction expansions associated with 1 d periodic differential operators of order 2 n
We prove an explicit formula for the spectral expansions in L(R) generated by selfadjoint differential operators (−1) d dx2n + n−1
متن کاملar X iv : m at h / 06 06 28 9 v 1 [ m at h . A G ] 1 2 Ju n 20 06 On correspondences of a K 3 surface with itself . IV
Let X be a K3 surface with a polarization H of the degree H 2 = 2rs, r, s ≥ 1, and the isotropic Mukai vector v = (r, H, s) is primitive. The moduli space of sheaves over X with the isotropic Mukai vector (r, H, s) is again a K3 surface, Y. In [11] the second author gave necessary and sufficient conditions in terms of Picard lattice N (X) of X when Y is isomorphic to X (some important particula...
متن کاملar X iv : m at h / 06 06 28 9 v 2 [ m at h . A G ] 1 9 Ju n 20 06 On correspondences of a K 3 surface with itself . IV
Let X be a K3 surface with a polarization H of the degree H 2 = 2rs, r, s ≥ 1, and the isotropic Mukai vector v = (r, H, s) is primitive. Moduli space of sheaves over X with the isotropic Mukai vector (r, H, s) is again a K3 surface, Y. In [12] second author gave necessary and sufficient conditions in terms of Picard lattice N (X) of X when Y is isomorphic to X (important particular cases were ...
متن کاملar X iv : m at h / 06 06 31 2 v 1 [ m at h . A C ] 1 3 Ju n 20 06 ASYMPTOTIC BEHAVIOR OF MULTIGRADED REGULARITY
Let S be a standard N k-graded polynomial ring over a field K, let I be a multigraded homogeneous ideal of S, and let M be a finitely generated Z k-graded S-module. We prove that the resolution regularity, a multigraded variant of Castelnuovo-Mumford regularity, of I n M is asymptotically a linear function. This shows that the well known Z-graded phenomenon carries to multigraded situation.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006