Abstract
Products and coproducts in the category <i>S</i>(<i>B</i>) of Segal topological algebras
Highlights
The study of Segal topological algebras started in [1]
In the present paper we show that all coproducts of two objects of the category S(B) always exist
While the coproducts exist always and have a form similar to the form of coproducts in the category of algebras, the products might or might not exist and have a bit different description, similar to the description of a Whitney sum known in the theory of fibre spaces
Summary
The study of Segal topological algebras started in [1]. It was followed by [2], where the category S(B) of Segal topological algebras was represented as triples (A, f , B) where B was fixed. Suppose that (A, f , B), (C, g, B) ∈ Ob(S(B)), let T be the tensor algebra of A and C and define a map hT : T → B as follows: n ki Ni hT (t) = ∑ ∑ ∏ hT (ti, j,l) i=1 j=1 l=1 for every element
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