论文标题
定期有效的常规类别
Regular and effective regular categories of locales
论文作者
论文摘要
我们研究了有关某些空间的规律性和有效性的两个众所周知的结果的类别的类似物。我们表明，紧凑的常规环境类别是有效的（= barr-exact）。我们还表明，只要它在Hausdorff Locales中具有核心，因此紧凑的Hausdorff Locales类别是常规的。我们不诉诸存在点的存在（这将使这两个结果微不足道），而要依赖于对主体内部逻辑中有效的方法的处理。在结果的过程中，我们得出了B. Day和R. Street的结果的概括，该类别的规律性是规律性的，该类别包含在有限限制和colimits下封闭的密集规则子类别，并满足了与适当的colimits合适的回扣的某些兼容性条件。
We examine the analogues for the respective categories of locales of two well-known results about regularity and effectiveness of some categories of spaces. We show that the category of compact regular locales is effective regular (=Barr-exact). We also show that the category of compactly generated Hausdorff locales is regular, provided that it is coreflective within Hausdorff locales. We do not appeal to the existence of points (which would render the two results trivial) but rely on the treatment of the subject by methods that are valid in the internal logic of a topos. On the course to the result about compactly generated locales we arrive at a generalization of a result of B. Day and R. Street, deriving regularity for a cocomplete category containing a dense regular subcategory closed under finite limits and colimits and satisfying a certain compatibility condition of pullbacks with appropriate colimits.
