关于主生成Q-模的一般性和斜局部同胚的特殊性
On principally generated Q-modules in general, and skew local homeomorphisms in particular
摘要：
小量子群Q上的有序层已经被定义为Q-丰富范畴结构;它们形成局部有序范畴Ord（Q）。Ord（Q）上的自由余补KZ-定理把Q-模的quantaloid Mod（Q）作为Eilenberg-Moore代数的范畴。本文给出了Kleisli代数的一个内在描述：我们称之为“局部主生成Q-模”。我们证明了Ord（Q）与局部主生成Q-模和左伴随模态射的2-范畴是双等价的。局部主生成模的例子在locale X上被详细地给出：将X-模与切片范畴Loc/X的对象联系起来，我们证明了X上的有序层对应于“斜局部同胚到X”（就像X上的层对应于局部同胚到X）。
英文摘要：
Ordered sheaves on a small quantaloid Q have been defined in terms of Q-enriched categorical structures; they form a locally ordered category Ord(Q). The free-cocompletion KZ-doctrine on Ord(Q) has Mod(Q), the quantaloid of Q-modules, as category of Eilenberg-Moore algebras. In this paper we give an intrinsic description of the Kleisli algebras: we call them the 'locally principally generated Q-modules'. We deduce that Ord(Q) is biequivalent to the 2-category of locally principally generated Q-modules and left adjoint module morphisms. The example of locally principally generated modules on a locale X is worked out in full detail: relating X-modules to objects of the slice category Loc/X, we show that ordered sheaves on X correspond with 'skew local homeomorphisms into X' (like sheaves on X correspond with local homeomorphisms into X).
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