Geodesic
Homology theory in the alternative set theory I. Algebraic preliminaries
Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 1, pp. 75-93.

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The notion of free group is defined, a relatively wide collection of groups which enable infinite set summation (called {\bf commutative $\pi$-group}), is introduced. Commutative $\pi$-groups are studied from the set-theoretical point of view and from the point of view of free groups. Commutativity of the operator which is a special kind of inverse limit and factorization, is proved. Tensor product is defined, commutativity of direct product (also a free group construction and tensor product) with the special kind of inverse limit is proved. Some important examples of tensor product are computed.
Classification : 03E70, 03H05, 18G99, 20F99, 55N99
Keywords: alternative set theory; commutative $\pi $-group; free group; inverse system of Sd-classes and Sd-maps; prolongation; set-definable; tensor product; total homomorphism 
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     title = {Homology theory in the alternative set theory {I.} {Algebraic} preliminaries},
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Guričan, Jaroslav. Homology theory in the alternative set theory I. Algebraic preliminaries. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 1, pp. 75-93. http://geodesic.mathdoc.fr/item/CMUC_1991__32_1_a8/