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T 2 and T 3 objects at p in the category of proximity spaces

Muammer Kula, Samed Özkan (2020)

Mathematica Bohemica

In previous papers, various notions of pre-Hausdorff, Hausdorff and regular objects at a point p in a topological category were introduced and compared. The main objective of this paper is to characterize each of these notions of pre-Hausdorff, Hausdorff and regular objects locally in the category of proximity spaces. Furthermore, the relationships that arise among the various Pre T 2 , T i , i = 0 , 1 , 2 , 3 , structures at a point p are investigated. Finally, we examine the relationships between the generalized separation...

The Brauer category and invariant theory

Gustav I. Lehrer, R. B. Zhang (2015)

Journal of the European Mathematical Society

A category of Brauer diagrams, analogous to Turaev’s tangle category, is introduced, a presentation of the category is given, and full tensor functors are constructed from this category to the category of tensor representations of the orthogonal group O ( V ) or the symplectic group Sp ( V ) over any field of characteristic zero. The first and second fundamental theorems of invariant theory for these classical groups are generalised to the category theoretic setting. The major outcome is that we obtain presentations...

The notion of closedness in topological categories

Mehmet Baran (1993)

Commentationes Mathematicae Universitatis Carolinae

In [1], various generalizations of the separation properties, the notion of closed and strongly closed points and subobjects of an object in an arbitrary topological category are given. In this paper, the relationship between various generalized separation properties as well as relationship between our separation properties and the known ones ([4], [5], [7], [9], [10], [14], [16]) are determined. Furthermore, the relationships between the notion of closedness and strongly closedness are investigated...

The Roquette category of finite p -groups

Serge Bouc (2015)

Journal of the European Mathematical Society

Let p be a prime number. This paper introduces the Roquette category ℛ p of finite p -groups, which is an additive tensor category containing all finite p -groups among its objects. In ℛ p , every finite p -group P admits a canonical direct summand ∂ P , called the edge of P . Moreover P splits uniquely as a direct sum of edges of Roquette p -groups, and the tensor structure of ℛ p can be described in terms of such edges. The main motivation for considering this category is that the additive functors from ℛ p to...

Topological balls

Michael Barr, Heinrich Kleisli (1999)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

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