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The formulation of the section titled "In general topology" is vague and incorrect. The closed interval of the real line is indeed a cogenerator in the category of completely regular spaces, and the same goes for the open and half-open intervals. However, no interval is injective as an object of
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The definitions given for generator and cogenerator objects in categories having a zero object (as such an unnecessary restriction) are incorrect. They would imply that
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this category, since there exists a continuous map into it defined on the circle minus a point which cannot be extended continuously to the entire circle.
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The example about cogenerators in a category of topological spaces doesn't quite fit the definition, as the category doesn't have a zero object.
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OK - this is mentioned in the book of Barr and Wells as an example, but I was worrying about whether it was quite right.
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supposed to be a generator? Do we know that the category has a generator? Most importantly, what is the reference?
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Knowledge. If you would like to participate, please visit the project page, where you can join
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The article does not actually provide a definition for the concept of injective cogenerator.
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This rather isolated page is densely written, and really needs to be taken in hand.
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is both a generator and a cogenerator in the category of modules over the ring
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supposed to be here? Is it supposed to be true for any
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