Displaying similar documents to “Duality for CCD lattices.”

On the L -valued categories of L - E -ordered sets

Olga Grigorenko (2012)

Kybernetika

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The aim of this paper is to construct an L -valued category whose objects are L - E -ordered sets. To reach the goal, first, we construct a category whose objects are L - E -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 L -valued category. Further we investigate the properties of this category, namely, we observe some special...

Totality of product completions

Jiří Adámek, Lurdes Sousa, Walter Tholen (2000)

Commentationes Mathematicae Universitatis Carolinae

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Categories whose Yoneda embedding has a left adjoint are known as total categories and are characterized by a strong cocompleteness property. We introduce the notion of multitotal category 𝒜 by asking the Yoneda embedding 𝒜 → [ 𝒜 o p , 𝒮 e t ] to be right multiadjoint and prove that this property is equivalent to totality of the formal product completion Π 𝒜 of 𝒜 . We also characterize multitotal categories with various types of generators; in particular, the existence of dense generators is inherited by the...