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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.

$𝔙$ -Cat is locally presentable or locally bounded if $𝔙$ is so.

Kelly, G.M., Lack, Stephen (2001)

Theory and Applications of Categories [electronic only]

$(E, M)$ -functors and $M$ -universal initial completions

Hubertus W. Bargenda (1990)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

$𝒦$ -purity and orthogonality.

Hébert, Michel (2004)

Theory and Applications of Categories [electronic only]

$𝒯$ -semiring pairs

Jaiung Jun, Kalina Mincheva, Louis Rowen (2022)

Kybernetika

We develop a general axiomatic theory of algebraic pairs, which simultaneously generalizes several algebraic structures, in order to bypass negation as much as feasible. We investigate several classical theorems and notions in this setting including fractions, integral extensions, and Hilbert's Nullstellensatz. Finally, we study a notion of growth in this context.

2-categorical tools in the theory of concrete categories

Rosický, Jiří (1977)

Abstracta. 5th Winter School on Abstract Analysis

...-Extensions of Topological Spaces II.

T. Thrivikraman (1975)

Monatshefte für Mathematik

$𝔤$ -quasi-Frobenius Lie algebras

David N. Pham (2016)

Archivum Mathematicum

A Lie version of Turaev’s $\bar{G}$ -Frobenius algebras from 2-dimensional homotopy quantum field theory is proposed. The foundation for this Lie version is a structure we call a $𝔤$ -quasi-Frobenius Lie algebra for $𝔤$ a finite dimensional Lie algebra. The latter consists of a quasi-Frobenius Lie algebra $(𝔮, β)$ together with a left $𝔤$ -module structure which acts on $𝔮$ via derivations and for which $β$ is $𝔤$ -invariant. Geometrically, $𝔤$ -quasi-Frobenius Lie algebras are the Lie algebra structures associated to symplectic...

$μ$ -bicomplete categories and parity games

Luigi Santocanale (2002)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

For an arbitrary category, we consider the least class of functors containing the projections and closed under finite products, finite coproducts, parameterized initial algebras and parameterized final coalgebras, i.e. the class of functors that are definable by $μ$ -terms. We call the category $μ$ -bicomplete if every $μ$ -term defines a functor. We provide concrete examples of such categories and explicitly characterize this class of functors for the category of sets and functions. This goal is achieved...

μ-Bicomplete Categories and Parity Games

Luigi Santocanale (2010)

RAIRO - Theoretical Informatics and Applications

For an arbitrary category, we consider the least class of functors containing the projections and closed under finite products, finite coproducts, parameterized initial algebras and parameterized final coalgebras, i.e. the class of functors that are definable by μ-terms. We call the category μ-bicomplete if every μ-term defines a functor. We provide concrete examples of such categories and explicitly characterize this class of functors for the category of sets and functions. This goal is achieved...