学术报告
A Gluing of derived equivalences with bimodules
题目： A Gluing of derived equivalences with bimodules
报告人： Prof. Dr. Hideto Asashiba
(Shizuoka University, Shizuoka, Japan)
摘要: We fix a commutative ring k and a small category I with I_0 (resp. I_1) the class of objects (resp. morphisms). Consider the bicategory k-Catb of all small k-categories whose 1-morphisms are the bimodules over them and whose 2-morphisms are the bimodule morphisms (more precisely 1-morphisms from C to D are the D-C-bimodules M and the composite C —> D —> E is given by the tensor product over D). We define (a generalized version of) the Grothendieck construction Gr(X) of a lax functor X: I —> k-Catb,which enables us to construct new k-categories by tying k-categories X(i) (i in I_0) together with bimodules X(a) (a in I_1). In particular, this construction can present a triangular matrix algebra, or more generally the tensor algebra of a k-species. For a lax functor X: I —> k-Catb, we define its "module category" Mod X and its "derived module category" D(Mod X), both of which are again lax functors from I. We also define a notion of derived equivalences between lax functors I —> k-Catb. When k is a field, we can construct a derived equivalence between the Grothendieck constructions Gr(X) and Gr(X') of lax functors X, X': I —> k-Catb by gluing derived equivalences between X(i) and X'(i) (i in I_0) together with bimodules X(a) and X'(a) (a in I_1) if X and X' are derived equivalent.
时间：4月28日（周四）下午4:00-5:00
地点：首都师大北二区教学楼130教室
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