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Super, Quantum and Non-Commutative Species

Volume 8, Number 1 (2009), 90 - 130

Super, Quantum and Non-Commutative Species

Price: $20.00

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.