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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...

$T_{2}$ -frames and almost compact frames

Jan Paseka, Bohumil Šmarda (1992)

Czechoslovak Mathematical Journal

$T$ -algebras of the monad $L$ -Fuzz

Joachim Machner (1985)

Czechoslovak Mathematical Journal

$T o p^{o p}$ is a quasi-variety

Michael Barr, M. Cristina Pedicchio (1995)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

T-categories and some representation theorems

Bentley, H.L. (1973)

Portugaliae mathematica

Tenseurs et machines

René Guitart (1980)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Tensor product of partially-additive monoids.

A. Bahamonde (1985)

Semigroup forum

Tensor products in the category of graphs

Aleš Pultr (1970)

Commentationes Mathematicae Universitatis Carolinae

Tensor products in the category of topological spaces

Juraj Činčura (1979)

Commentationes Mathematicae Universitatis Carolinae

Ternary semigroups of morphisms of objects in categories

Antoni Chronowski, Miroslav Novotný (1995)

Archivum Mathematicum

In this paper the notion of a ternary semigroup of morphisms of objects in a category is introduced. The connection between an isomorphism of categories and an isomorphism of ternary semigroups of morphisms of suitable objects in these categories is considered. Finally, the results obtained for general categories are applied to the categories $𝐑𝐄𝐋 n + 1$ and $𝐀𝐋𝐆 n$ which were studied in [5].

Ternary structures and groupoids

Miroslav Novotný (1991)

Czechoslovak Mathematical Journal

The 3-by-3 lemma for regular Goursat categories.

Lack, Stephen (2004)

Homology, Homotopy and Applications

The algebraic theory of compact Lawson semilattices Applications of Galois connections to compact semilattices [Book]

Karl Heinrich Hofmann, Albert Stralka (1976)

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 Cantor-Bernstein theorem for functors

Věra Trnková, Václav Koubek (1973)

Commentationes Mathematicae Universitatis Carolinae

The cartesian closed hull of the category of approach spaces

E. Lowen-Colebunders, R. Lowen, M. Nauwelaerts (2001)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

The cartesian closed topological hull of the category of completely regular filterspaces

H. L. Bentley, E. Lowen-Colebunders (1992)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

The categories of presheaves containing any category of algebras [Book]

V. Trnková, J. Reiterman (1975)

The category of Banach spaces in sheaves

Joan Wick Pelletier, Robert D. Rosebrugh (1979)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

The category of groupoid graded modules

Patrik Lundström (2004)

Colloquium Mathematicae

We introduce the abelian category R-gr of groupoid graded modules and give an answer to the following general question: If U: R-gr → R-mod denotes the functor which associates to any graded left R-module M the underlying ungraded structure U(M), when does either of the following two implications hold: (I) M has property X ⇒ U(M) has property X; (II) U(M) has property X ⇒ M has property X? We treat the cases when X is one of the properties: direct summand, free, finitely generated, finitely presented,...

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