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𝒯 0 - and 𝒯 1 -reflections

Maria Manuel Clementino (1992)

Commentationes Mathematicae Universitatis Carolinae

In an abstract category with suitable notions of subobject, closure and point, we discuss the separation axioms T 0 and T 1 . Each of the arising subcategories is reflective. We give an iterative construction of the reflectors and present characteristic examples.

𝒟 -modules et faisceaux pervers dont le support singulier est un croisement normal

André Galligo, Michel Granger, Philippe Maisonobe (1985)

Annales de l'institut Fourier

Dans cet article on étudie les 𝒟 -modules dont le support singulier est un croisement normal dans C n , par l’intermédiaire de la catégorie équivalente de faisceaux pervers. On montre qu’ils sont caractérisés, à isomorphisme près, par la donnée suivante : un hypercube constitué par des espaces vectoriels de dimension finie F I indexés par les parties de { 1 , ... , n } , et des applications linéaires F I F I { i } soumises à certaines conditions de commutativité et d’inversibilité. Ce résultat est exprimé sous forme d’une équivalence...

( n , d ) -injective covers, n -coherent rings, and ( n , d ) -rings

Weiqing Li, Baiyu Ouyang (2014)

Czechoslovak Mathematical Journal

It is known that a ring R is left Noetherian if and only if every left R -module has an injective (pre)cover. We show that ( 1 ) if R is a right n -coherent ring, then every right R -module has an ( n , d ) -injective (pre)cover; ( 2 ) if R is a ring such that every ( n , 0 ) -injective right R -module is n -pure extending, and if every right R -module has an ( n , 0 ) -injective cover, then R is right n -coherent. As applications of these results, we give some characterizations of ( n , d ) -rings, von Neumann regular rings and semisimple rings....

A Borel topos

Donovan H. Van Osdol (1981)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

A categorical account of the localic closed subgroup theorem

Christopher Townsend (2007)

Commentationes Mathematicae Universitatis Carolinae

Given an axiomatic account of the category of locales the closed subgroup theorem is proved. The theorem is seen as a consequence of a categorical account of the Hofmann-Mislove theorem. The categorical account has an order dual providing a new result for locale theory: every compact subgroup is necessarily fitted.

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