Free braided pivotal categories

• Main Author: Oury, David.
• Format: Others
• Language: en
• Published: McGill University 2005
• Subjects: Mathematics.
• Online Access: http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=97984

Free braided pivotal categories are equivalent to free strict monoidal categories on a graph with relations. This is important in the study of knot invariants in that new invariants can be constructed simply by finding suitable strict monoidal categories. === This is demonstrated by developing the formal language of strict monoidal categories on a graph with relations, creating categories with relations corresponding to the Reidemeister moves of knot theory and finally showing that these categories are in fact free braided pivotal categories and further equivalent to the categories of link diagrams from knot theory.