Group Objects and Internal Categories
By Magnus Forrester-Barker. 2002
51 citations recorded by the source corpus.
Algebraic structures such as monoids, groups, and categories can be formulated within a category using commutative diagrams. In many common categories these reduce to familiar cases. In particular, group objects in Grp are abelian groups, while internal categories in Grp are equivalent both to group objects in Cat and to crossed modules of groups. In this exposition we give an elementary introduction to some of the key concepts in this area.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/0ae0454ace9c3c0d8045fa9c618ef3a06dde05a7
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In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Integrating $L_\infty $-algebras (2006, methodology): “trict Lie 2-group, constructed using the loop group of Gand its basic central extension by S1. Strict 2-groups, i.e. group objects in the category of groupoids, are equivalent to crossed modules [4], [10]. A crossed module consists of two groups H 0, H 1, a homomorphism ∂: H 1 →H 0, and an action H ”