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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,
If we take as D the empty doctrine, we have a duality between the 2-category of small Cauchy complete categories, functors and natural transformations, and the 2-category of
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
As a small dense subcategory representing finitely presentable objects we can choose categories on finitely many objects subject to a finite set of commutativity
Day, On closed categories of functors, Lecture Notes in Mathematics 137 (Springer-Verlag, Berlin 1970), pp... Day, On closed categories of functors II, Lecture Notes in Mathematics
Davenport pointed out the connection between this constant and Algebraic Number Theory, where it is used to measure the maximal number of ideal classes which can occur in
Of course, under the equivalence given above, the tensor product of double categories withconnection corresponds to the Gray tensor product of 2-categories, except that, from the
Using some relations between the branching homology of some particular ω-categories and the usual simplicial homology of some associated ω-categories (Theorem 5.5), the behaviour of
