Category Theory in Physics, Mathematics, and Philosophy by Unknown

Author:Unknown
Language: eng
Format: epub
ISBN: 9783030308964
Publisher: Springer International Publishing

5.2.2 Coproducts in the Same Categories

In contrast to the preceding, coproducts may be markedly different from each other. This is clearly shown in the following Table 5.1.Table 5.1In the left-hand column there are symbols of categories together with concise descriptions of their objects and morphisms. In the middle column, for each category there is a description of products. Conspicuously, the cartesian product appears in each cell with exception of Banach spaces and commutative -algebras (however this difference disappears when one changes the definition of the carrier of the object taking the closed unit ball instead of the whole vector space). In the right-hand column there are descriptions of respective coproducts. There are six distinct types of them: coproducts related to the disjoint union ; free products of groups; coproducts related to directs sums of abelian groups; coproducts related to tensor products of rings; -sums; a specific construction for automata

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