Super, quantum and non-commutative species Export

@article{citeulike:4650600, abstract = {We introduce an approach to the categorification of rings, via the notion of distributive categories with negative objects, and use it to lay down categorical foundations for the study of super, quantum and non-commutative combinatorics. Via the usual duality between algebra and geometry, these constructions provide categorifications for various types of affine spaces, thus our works may be regarded as a starting point towards the construction of a categorical geometry.}, archivePrefix = {arXiv}, author = {Diaz, Rafael and Pariguan, Eddy}, citeulike-article-id = {4650600}, citeulike-linkout-0 = {http://arxiv.org/abs/math/0509674}, citeulike-linkout-1 = {http://arxiv.org/pdf/math/0509674}, eprint = {math/0509674}, keywords = {category-theory, geometry, mathematics, quantum}, month = {May}, posted-at = {2009-05-28 19:02:39}, priority = {2}, title = {Super, quantum and non-commutative species}, url = {http://arxiv.org/abs/math/0509674}, year = {2009} }

TY - JOUR ID - citeulike:4650600 L3 - citeulike-article-id:4650600 N2 - We introduce an approach to the categorification of rings, via the notion of distributive categories with negative objects, and use it to lay down categorical foundations for the study of super, quantum and non-commutative combinatorics. Via the usual duality between algebra and geometry, these constructions provide categorifications for various types of affine spaces, thus our works may be regarded as a starting point towards the construction of a categorical geometry. TI - Super, quantum and non-commutative species KW - category-theory KW - geometry KW - mathematics KW - quantum AU - Diaz, Rafael AU - Pariguan, Eddy PY - 2009/May/27/ UR - http://arxiv.org/abs/math/0509674 ER -