Contravariantly Finite Subcategories and Adjunctions

• 来源期刊: 代数集刊（英文版）
• 学科: 数学
• 关键词: adjoint pair contravariantly finite subcategory covariantly finite subcategory
• 年，卷（期）: 2001,（3）
• 页码范围: 307-314
• 页数: 8页
• 分类号: O1
• 语种: 英文

摘要

Let (F, G) be an adjoint pair from a category 4 to a category B. The contravariantly finiteness of subcategories is proved to be preserved by F, and the covariantly finiteness of subcategories is preserved by F under some additional conditions. If A and B are length categories, G(Im (F)) = Im (G), and F is full,then the inclusion i: Im (F) → B has a right adjoint. This gives a partial answer to a question posed by Auslander and Reiten in [2].