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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