3-types of simplicial groups and braided regular crossed modules

Arvasi, Z.; Ulualan, Erdal

doi:10.4310/hha.2007.v9.n1.a5

Cited by 6 publications

(4 citation statements)

References 21 publications

(27 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [1], the relationship between braided crossed modules and reduced simplicial groups was reproved by use of the functions F α,β . Also in [4], this construction was extended to the 'regularity'. That is, 'a description of the passage from a simplicial group to a braided regular crossed module by use of the functions F α,β '.…”

Section: Braided Categorical Groups and Crossed Modulesmentioning

confidence: 99%

Braiding for internal categories in the category of whiskered groupoids and simplicial groups

Ulualan¹,

Pak²

2013

Turkish Journal of Mathematics

View full text Add to dashboard Cite

Section: Braided Categorical Groups and Crossed Modulesmentioning

confidence: 99%

Braiding for internal categories in the category of whiskered groupoids and simplicial groups

Ulualan¹,

Pak²

2013

Turkish Journal of Mathematics

View full text Add to dashboard Cite

“…In the terminology of [BG89a], we would call AUT(C) a braided, regular crossed complex. See also [AU07] for related material in the crossed module case. In [BT97], crossed differential algebras are called crossed chain algebras.…”

Section: Braided Crossed Complexes and Automorphismsmentioning

confidence: 99%

Possible connections between whiskered categories and groupoids, many object Leibniz algebras, automorphism structures and local-to-global questions

Brown

2007

Preprint

View full text Add to dashboard Cite

We define the notion of whiskered categories and groupoids, showing that whiskered groupoids have a commutator theory. So also do whiskered R-categories, thus answering questions of what might be 'commutative versions' of these theories. We relate these ideas to the theory of Leibniz algebras, but the commutator theory here does not satisfy the Leibniz identity. We also discuss potential applications and extensions, for example to resolutions of monoids.

show abstract

“…As a 2-dimensional analog, we can say that if C is crossed module, then Aut(C) has a braided regular crossed module structure defined by Brown and Gilbert [8], see also [9] for this structure. For the reduced cases of this structure in other contexts, see [10,11].…”

Section: Introductionmentioning

confidence: 99%

Whiskered Groupoids and Crossed Modules with Diagrams

Güler,

Ulualan

2024

Journal of New Theory

View full text Add to dashboard Cite

In this study, we investigate the relationships between the category of crossed modules of groups and the category of whiskered groupoids. Our first aim is to construct a crossed module structure over groups from a whiskered groupoid with the objects set - a group (regular groupoid) - using the usual functor between the categories of crossed modules and cat groups. Conversely, the second aim is to construct a whiskered groupoid structure with the objects set, which is a group, from a crossed module of groups. While establishing this relationship, we frequently used arrow diagrams representing morphisms to make the axioms more comprehensible. We provide the conditions for the bimorphisms in a whiskered groupoid and give the relations between this structure and internal groupoids in the category of whiskered groupoids with the objects set as a group.

show abstract

3-types of simplicial groups and braided regular crossed modules

Abstract: In this work, we explain the relations among braided regular crossed modules, simplicial groups, 2-crossed modules, quadratic modules and crossed squares, and the role of hypercrossed complex pairings in these structures.

Cited by 6 publications

References 21 publications

Braiding for internal categories in the category of whiskered groupoids and simplicial groups

Braiding for internal categories in the category of whiskered groupoids and simplicial groups

Possible connections between whiskered categories and groupoids, many object Leibniz algebras, automorphism structures and local-to-global questions

Whiskered Groupoids and Crossed Modules with Diagrams

Contact Info

Product

Resources

About