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INSTANCES AND RAMIFICATIONS OF THE SEMI-ADJOINT SITUATION I. PRESTABLE REFLECTION AND SYMMETRIC UNADS

 

作者: K.A. Hardie,  

 

期刊: Quaestiones Mathematicae  (Taylor Available online 1977)
卷期: Volume 2, issue 1-3  

页码: 147-158

 

ISSN:1607-3606

 

年代: 1977

 

DOI:10.1080/16073606.1977.9632539

 

出版商: Taylor & Francis Group

 

关键词: 18C15;18605

 

数据来源: Taylor

 

摘要:

It is well known that there is a one to one correspondence between idempotent monads in a category and reflective subcategories. In this paper it is examined what replaces the reflective subcategory if the idempotent monad is replaced (a) by a monad and (b) by a symmetric unad. It is shown that in case (a) one obtains the weakly reflective subcategory of objects injective relative to the functor part of the monad. In case (b) one obtains a proto-reflection and it is shown that (for complete categories) the associated orthogonal subcategory is reflective if and only if there exists a free monad associated to the unad.

 

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