An -category is a category equipped with an -module structure on each hom set such that the composition is -bilinear. More precisely, let us assume for instance that we are given a commutative ring with identity. Then a small -category–or equivalently an -algebroid– will be defined as a category enriched in the monoidal category of -modules, with respect to the monoidal structure of tensor product. This means simply that for all objects of , the set is given the structure of an -module, and composition is –bilinear, or is a morphism of -modules .
- 1 R. Brown and G. H. Mosa: Double algebroids and crossed modules of algebroids, University of Wales–Bangor, Maths Preprint, 1986.
- 2 G. H. Mosa: Higher dimensional algebroids and Crossed complexes, PhD thesis, University of Wales, Bangor, (1986). (supervised by R. Brown).
- 3 I. C. Baianu , James F. Glazebrook, and Ronald Brown. 2009. Algebraic Topology Foundations of Supersymmetry and Symmetry Breaking in Quantum Field Theory and Quantum Gravity: A Review. SIGMA 5 (2009), 051, 70 pages. , , http://www.emis.de/journals/SIGMA/2009/051/Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
|Date of creation||2013-03-22 18:14:15|
|Last modified on||2013-03-22 18:14:15|
|Last modified by||bci1 (20947)|
|Defines||morphism of R-modules|
|Defines||extension of R-algebroids over rings|