Super, quantum and non-commutative species

Details Super, quantum and non-commutative species Super, quantum and non-commutative species

2005-09-28

arxiv.org/abs/math/0509674v3

African Diaspora Journal of Mathematics. Volume 8, Number 1, pp. 90-130 (2009)

Mathematics

Category Theory

43 pages, 12 figures

Scientific paper

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.

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