INSTANCES AND RAMIFICATIONS OF THE SEMI-ADJOINT SITUATION II. THE COMPARISON FUNCTOR
作者:
K.A. Hardie,
期刊:
Quaestiones Mathematicae
(Taylor Available online 1977)
卷期:
Volume 2,
issue 1-3
页码: 159-175
ISSN:1607-3606
年代: 1977
DOI:10.1080/16073606.1977.9632540
出版商: Taylor & Francis Group
关键词: 18C99;18A40;18C15;16A48
数据来源: Taylor
摘要:
If a functor U has a left co-unadjoint then U can be factored through a category of semad algebras. An analogue of the Beck monadicity theory is obtained. If R is a ring without a left unit but satisfying R2= R then the category of unitary left R-modules need not be monadic over Set. The forgetful functor has, however, a left co-unadjoint for which a comparison functor is an equivalence of categories. Another example of a semadic functor is obtained by composing the forgetful functor from Abelian groups to Set with the doubling functor. The semi-adjoint situations in the senses of Medvedev and Davis are examined.
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