Geodesic
Product of proper shape equivalences over finite coverings is an equivalence
Serdica Mathematical Journal, Tome 44 (2018) no. 1-2, pp. 121-136

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In this paper we prove that in the category of proper shape over finite coverings from ShpF (X) = ShpF (X′) and ShpF (Y ) = ShpF (Y′) it follows that ShpF (X × Y ) = ShpF (X′ × Y′). Also, we give an example in which the product of two morphisms is not morphism in the category of proper shape.
Keywords: Product of morphisms, proper proximate sequence over finite coverings, intrinsic shape, finite covering, shape of product, 54C56 
Shekutkovski, Nikita; Abdulla, Buklla. Product of proper shape equivalences over finite coverings is an equivalence. Serdica Mathematical Journal, Tome 44 (2018) no. 1-2, pp. 121-136. http://geodesic.mathdoc.fr/item/SMJ2_2018_44_1-2_a5/
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     title = {Product of proper shape equivalences over finite coverings is an equivalence},
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     pages = {121--136},
     year = {2018},
     volume = {44},
     number = {1-2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SMJ2_2018_44_1-2_a5/}
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