On Sifted Colimits and Generalized Varieties
On Sifted Colimits and Generalized Varieties
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关于筛选余界和广义簇
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
J. Rosick
中科院分区：
文献类型：
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作者：
J. A. Amek;J. Rosick
过滤余极限，即方案 D 上的余极限，使得 Set 中的 D-colimit 与 nite 极限交换，对筛选余极限具有自然的泛化：这些是方案 D 上的余极限，使得 Set 中的 D-colimit 与 nite 乘积交换。一个重要的例子：reeexive 协均衡器是经过筛选的余极限。广义变体被视为小类别在筛选余限下的自由补全（类似于nitelyaccesscategories，它是小类别的自由筛选余限补全）。在完整的类别中，广义的品种正是品种。更多示例：字段类别、线性有序集合类别、非空集合类别。
Filtered colimits, i.e., colimits over schemes D such that D-colimits in Set commute with nite limits, have a natural generalization to sifted colimits: these are colimits over schemes D such that D-colimits in Set commute with nite products. An important example: reeexive coequalizers are sifted colimits. Generalized varieties are deened as free completions of small categories under sifted-colimits (analogously to nitely accessible categories which are free ltered-colimit completions of small categories). Among complete categories, generalized varieties are precisely the varieties. Further examples: category of elds, category of linearly ordered sets, category of nonempty sets.