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.
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.
| Original language | English |
|---|---|
| Pages (from-to) | 90-190 |
| Number of pages | 43 |
| Journal | African Diaspora Journal of Mathematics |
| Volume | 8 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2009 |