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Article

Kernels and Cokernels in the Category of Augmented Involutive Stereotype Algebras

We prove several properties of kernels and cokernels in the category of augmented involutive
stereotype algebras: 1) this category has kernels and cokernels, 2) the cokernel is preserved under the
passage to the group stereotype algebras, and 3) the notion of cokernel allows to prove that the continuous
envelope Env C*(Z · K) of the group algebra of a compact buildup of an abelian locally compact group
is an involutive Hopf algebra in the category of stereotype spaces (Ste, \odot ). The last result plays an
important role in the generalization of the Pontryagin duality for arbitrary Moore groups.