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The category of compactifications and its coreflections

Anthony W. Hager, Brian Wynne (2022)

Commentationes Mathematicae Universitatis Carolinae

We define “the category of compactifications”, which is denoted CM, and consider its family of coreflections, denoted corCM. We show that corCM is a complete lattice with bottom the identity and top an interpretation of the Čech–Stone β . A c corCM implies the assignment to each locally compact, noncompact Y a compactification minimum for membership in the “object-range” of c . We describe the minimum proper compactifications of locally compact, noncompact spaces, show that these generate the atoms...

The free adjunction

Stephen Schanuel, Ross Street (1986)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Totality of product completions

Jiří Adámek, Lurdes Sousa, Walter Tholen (2000)

Commentationes Mathematicae Universitatis Carolinae

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 formal product...

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