Products in Categories without Uniqueness of cod and dom

The paper introduces Cartesian products in categories without uniqueness of cod and dom. It is proven that set-theoretical product is the product in the category Ens [7].This work has been supported by the Polish Ministry of Science and Higher Education project “Managing a Large Repository of Computer-verified Mathematical Knowledge” (N N519 385136).Institute of Informatics, University of Białystok, Sosnowa 64, 15-887 Białystok PolandGrzegorz Bancerek. König’s theorem. Formalized Mathematics, 1(3):589-593, 1990.Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.Beata Madras. Basic properties of objects and morphisms. Formalized Mathematics, 6(3):329-334, 1997.Zbigniew Semadeni and Antoni Wiweger. Wstęp do teorii kategorii i funktorów, volume 45 of Biblioteka Matematyczna. PWN, Warszawa, 1978.Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.Andrzej Trybulec. Many sorted sets. Formalized Mathematics, 4(1):15-22, 1993.Andrzej Trybulec. Categories without uniqueness of cod and dom. Formalized Mathematics, 5(2):259-267, 1996.Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990

Coproducts in Categories without Uniqueness of cod and dom

The paper introduces coproducts in categories without uniqueness of cod and dom. It is proven that set-theoretical disjoint union is the coproduct in the category Ens [9].Goliński Maciej - Institute of Informatics University of Białystok Sosnowa 64, 15-887 Białystok PolandKorniłowicz Artur - Institute of Informatics University of Białystok Sosnowa 64, 15-887 Białystok PolandGrzegorz Bancerek. König’s theorem. Formalized Mathematics, 1(3):589-593, 1990.Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.Artur Korniłowicz. Products in categories without uniqueness of cod and dom. Formalized Mathematics, 20(4):303-307, 2012. doi:10.2478/v10037-012-0036-7.Beata Madras. Basic properties of objects and morphisms. Formalized Mathematics, 6 (3):329-334, 1997.Beata Perkowska. Free many sorted universal algebra. Formalized Mathematics, 5(1): 67-74, 1996.Zbigniew Semadeni and Antoni Wiweger. Wstęp do teorii kategorii i funktorów, volume 45 of Biblioteka Matematyczna. PWN, Warszawa, 1978.Andrzej Trybulec. Categories without uniqueness of cod and dom. Formalized Mathematics, 5(2):259-267, 1996.Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.Andrzej Trybulec. Many sorted sets. Formalized Mathematics, 4(1):15-22, 1993.Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990