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In [2], classes of objects injective with respect to a set M of morphisms of a locally presentable category K were characterized: they are precisely the classes closed under products,
Namely, new factorization systems are constructed on the categories of Abelian groups (more generally, on any Abelian category), groups with unary operators, locally com- pact
A ring is an abelian object in the category of rings if and only if it has zero multiplication; the same is true for non-associative rings, for commutative rings, for Lie algebras,
Consider the case when V is locally finitely presentable as a closed category in the sense of [Kel82-2], and Φ is the class of finite weights as described there; this includes the
Note: unital, strongly unital and subtractive categories are all pointed categories, and the morphisms 0 in the diagrams in the table represent zero morphisms in a pointed category;
A pointed regular category is subtractive if and only if every span in it is subtractive, and moreover, the functor S not only preserves but also reflects subtractive spans..
Since sums are filtered conical colimits of finite sums and finite sums are absolute (as biproducts), every finitely accessible preadditive category has arbitrary small sums..
The class is described there as, roughly speaking, the smallest class of groups containing both locally compact abelian groups and nuclear topological vector spaces and that is
