A diagrammatic presentation of the category 3Cob

A category equivalent to the category of 3-dimensional cobordisms is defined in terms of planar diagrams. The operation of composition in this category is completely described via these diagrams.Comment: 26 page

A diagrammatic calculus for categorical quantum protocols

We propose an explicit realisation of a category with enough structure to check validity of certain class of quantum protocols. This category is based on the category of 1-dimensional cobordisms. A coherence result proves that it fulfils all desired conditions.Comment: 24 pages + appendix; continuation and application of arXiv:2001.0973

Proofs and surfaces

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