اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدGalois and universal universal coverings of linear categories and fibre products
129
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Let $k$ be a commutative ring. We study the behaviour of coverings of $k$-categories through fibre products and find a criterion for a covering to be Galois or universal.
قيم البحث
اقرأ أيضاً
We consider categories over a field $k$ in order to prove that smash extensions and Galois coverings with respect to a finite group coincide up to Morita equivalence of $k$-categories. For this purpose we describe processes providing Morita equivalen
ces called contraction and expansion. We prove that composition of these processes provides any Morita equivalence, a result which is related with the karoubianisation (or idempotent completion) and additivisation of a $k$-category.
We define an obstruction to the formality of a differential graded algebra over a graded operad defined over a commutative ground ring. This obstruction lives in the derived operadic cohomology of the algebra. Moreover, it determines all operadic Mas
sey products induced on the homology algebra, hence the name of derived universal Massey product.
Let k be an algebraically closed field of positive characteristic, and let W be the ring of infinite Witt vectors over k. Suppose G is a finite group and B is a block of kG of infinite tame representation type. We find all finitely generated kG-modul
es V that belong to B and whose endomorphism ring is isomorphic to k and determine the universal deformation ring R(G,V) for each of these modules.
Let $K$ be an algebraically closed field of characteristic zero. Algebraic structures of a specific type (e.g. algebras or coalgebras) on a given vector space $W$ over $K$ can be encoded as points in an affine space $U(W)$. This space is equipped wit
h a $text{GL}(W)$ action, and two points define isomorphic structures if and only if they lie in the same orbit. This leads to study the ring of invariants $K[U(W)]^{text{GL}(W)}$. We describe this ring by generators and relations. We then construct combinatorially a commutative ring $K[X]$ which specializes to all rings of invariants of the form $K[U(W)]^{text{GL}(W)}$. We show that the commutative ring $K[X]$ has a richer structure of a Hopf algebra with additional coproduct, grading, and an inner product which makes it into a rational PSH-algebra, generalizing a structure introduced by Zelevinsky. We finish with a detailed study of $K[X]$ in the case of an algebraic structure consisting of a single endomorphism, and show how the rings of invariants $K[U(W)]^{text{GL}(W)}$ can be calculated explicitly from $K[X]$ in this case.
When formulating universal properties for objects in a dagger category, one usually expects a universal property to characterize the universal object up to unique unitary isomorphism. We observe that this is automatically the case in the important sp
ecial case of C$^*$-categories, provided that one uses enrichment in Banach spaces. We then formulate such a universal property for infinite direct sums in C$^*$-categories, and prove the equivalence with the existing definition due to Ghez, Lima and Roberts in the case of W$^*$-categories. These infinite direct sums specialize to the usual ones in the category of Hilbert spaces, and more generally in any W$^*$-category of normal representations of a W$^*$-algebra. Finding a universal property for the more general case of direct integrals remains an open problem.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
