Generalising connected components

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• 作者：Joã ; o J. Xarez ^xarez@ua.pt
• 关键词：18A40 ; 18F20 ; 18E35 ; 18A32 ; 18B30 ; 20M07
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2012
• 期刊代码：35_00224049
• 类别：mt
• 出版时间：August, 2012
• 卷：216
• 期：8-9
• 页码：1823-1826
• 文件大小：194 K

摘要

Let be a reflection of a category with pullbacks into a full subcategory of . We introduce an additional structure on involving a pullback-preserving functor , which allows us to prove that the reflection is: (a) semi-left-exact if and only if it makes all connected components connected in an appropriate sense; (b) a reflection with stable units if and only if certain pullbacks of connected components are connected. This was previously done in the case where is the category of sets.