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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
The reason all coherent 2-groups with the same underlying weak 2-group are isomorphic is that we have defined a homomorphism of coherent 2-groups to be a weak monoidal functor,
We now use Theorem 2.6 to show that coherent unit actions on ABQR operads are preserved by the black square product and thus give rise to Hopf algebra structures on the free objects
As a consequence (see Corollary 6.2), we find that in the case of categories of distributive Ω 2 -groups, such as the categories of groups, rings, Lie algebras, and all the
Our proof of Theorem 2 follows by enumerating the degree sequences which fit into each of the five categories in Theorem 1 and then removing those that have been counted multiple
Hence if we use the balancing ergodic equality (see [4]) instead of the equality (1), then we get the uniqueness theorem for the ergodic maximal operator..
Theorem 1 implies that every solution of (1) with one zero is oscilla- tory to the right of this zero and the properties of solutions y without zeros follow from Theorem 2 and
In this subsection we shall extend the characterisation of distributions with non-negative De Pril transforms in terms of compound Poisson distributions from the univariate case to
