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If the pointed Set -functor T satisfies (BC) and V is a complete and cocomplete locally cartesian closed category, then Alg( T, V ) is a
Clearly this and Corollary 3.4 imply that the classes of Σ-structures closed under products, λ-directed colimits and λ-algebraically closed substructures are the ones axiomatizable
In order to give an example of a protomodular locally finitely presentable category C with a zero object which does not have a semi-abelian generator, we will present it as
As a small dense subcategory representing finitely presentable objects we can choose categories on finitely many objects subject to a finite set of commutativity
However, it cannot be completely lifted since in the last example we presented a locally finitely presentable category which, although it is a topos, has non- unique strict solutions
As explained in [Dav06b, Section 3], this model category structure is obtained from the local injective model structure on the category PreSpt( G − Sets df ) (the category of
We shall also introduce a notion of openness for these generalized mor- phisms and we shall prove that open generalized morphisms of locally compact Hausdorff second countable
In Section 6 we give a characterization of the locally cartesian closed regular categories D whose associated category of sheaves for the canonical topology (identified in Section 4)
