Talk:Reflective subcategory
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Integral domains
[edit]It is mentioned that fields are a reflexive subcategory of integral domains with reflector the functor that sends an integral domain to its fraction field. I think you should be more careful in formulating the property like this since you assume the morphisms in the category of integral domains are injective, in order to be able to define a morphism between fraction fields.
Reflectors as completion operators
[edit]The text now says "a reflector acts as a kind of completion operation." This is obvious for some cases, and is passable for some of the topological examples. But it seems wrong for nearly all the examples of reflective subcategories of groups or algebras. I think it is not a good general rule. Colin McLarty (talk) 00:51, 11 January 2015 (UTC)
Reflective subcategories of Set
[edit]For any algebraic theory T, the category of T-algebras in Set is a reflective subcategory of Set.
The above statement is not true. It has thus been removed from the article. In fact, there are only 3 full replete reflective subcategories of Set, namely the category itself, the subcategory of sets with at most one element (empty set and singletons), and the subcategory of sets with exactly one element (singletons). GeoffreyT2000 (talk, contribs) 02:35, 26 March 2017 (UTC)