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Jaiung Jun, Kalina Mincheva, Louis Rowen (2022)
Kybernetika
We develop a general axiomatic theory of algebraic pairs, which simultaneously generalizes several algebraic structures, in order to bypass negation as much as feasible. We investigate several classical theorems and notions in this setting including fractions, integral extensions, and Hilbert's Nullstellensatz. Finally, we study a notion of growth in this context.
Rudolf Fiby (1973)
Matematický časopis
Darald J. Hartfiel, Carlton J. Maxson (1975)
Czechoslovak Mathematical Journal
Crans, Sjoerd E. (1999)
Theory and Applications of Categories [electronic only]
Gábor Czédli, Eszter K. Horváth, Lajos Klukovits (2001)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
Jacques Penon (1973)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
Došen, Kosta (1998)
Publications de l'Institut Mathématique. Nouvelle Série
Pierre Ageron (1996)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
Gerhard Osius (1976)
Fundamenta Mathematicae
Marie-Paule Brameret, Michel Enguehard, Guy Renault (1964/1965)
Séminaire Dubreil. Algèbre et théorie des nombres
Clementino, Maria Manuel, Hofmann, Dirk, Tholen, Walter (2003)
Theory and Applications of Categories [electronic only]
Marco Riccardi (2015)
Formalized Mathematics
In the first part of this article we formalize the concepts of terminal and initial object, categorical product [4] and natural transformation within a free-object category [1]. In particular, we show that this definition of natural transformation is equivalent to the standard definition [13]. Then we introduce the exponential object using its universal property and we show the isomorphism between the exponential object of categories and the functor category [12].
David N. Pham (2016)
Archivum Mathematicum
A Lie version of Turaev’s -Frobenius algebras from 2-dimensional homotopy quantum field theory is proposed. The foundation for this Lie version is a structure we call a -quasi-Frobenius Lie algebra for a finite dimensional Lie algebra. The latter consists of a quasi-Frobenius Lie algebra together with a left -module structure which acts on via derivations and for which is -invariant. Geometrically, -quasi-Frobenius Lie algebras are the Lie algebra structures associated to symplectic...
Michael Barr (1986)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
Marco Riccardi (2013)
Formalized Mathematics
Category theory was formalized in Mizar with two different approaches [7], [18] that correspond to those most commonly used [16], [5]. Since there is a one-to-one correspondence between objects and identity morphisms, some authors have used an approach that does not refer to objects as elements of the theory, and are usually indicated as object-free category [1] or as arrowsonly category [16]. In this article is proposed a new definition of an object-free category, introducing the two properties:...
Antoni Wiweger (1976)
Pavel Pták (1972)
Commentationes Mathematicae Universitatis Carolinae
Ionescu, Lucian M. (2002)
International Journal of Mathematics and Mathematical Sciences
Fantham, P.H.H. (1970)
Portugaliae mathematica
Olga Grigorenko (2012)
Kybernetika
The aim of this paper is to construct an -valued category whose objects are --ordered sets. To reach the goal, first, we construct a category whose objects are --ordered sets and morphisms are order-preserving mappings (in a fuzzy sense). For the morphisms of the category we define the degree to which each morphism is an order-preserving mapping and as a result we obtain an -valued category. Further we investigate the properties of this category, namely, we observe some special objects, special...
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