Diagrammatic Algebra

Chapter 1. Introduction
Chapter 2. Elements
1. Sets, relations, and functions
2. Diagrammatics of linear algebra
3. Algebras
4. Simplfying, clarifying, and abstracting
5. General categorical principles
Chapter 3. Planar trivalent diagrams
1. Small categories
2. Trivalent graphs
Chapter 4. The multi-category FA
1. Composition of double arrows
2. Reversible arrows and additional double arrows
Chapter 5. Triple arrows for FA
1. Algebraic identities as double arrows
2. The category of double arrows
3. Critical aspects of weakly invertible 1-arrows
4. Coalgebra axioms as triple arrows
Chapter 6. Surfaces in 3-space
1. Guide to terminology
2. Objects, 1-arrows, and double arrows
3. Triple arrows in S
4. Quadruple arrows in the multi-category S
5. Functorial equivalent multi-categories
Chapter 7. Beyond surfaces
1. Different objects and arrows
2. Weak inverses revisited
3. Higher order arrows in FA
4. Restricting the collections of arrows
Chapter 8. Parentheses and so forth
1. The Temperley-Lieb algebra
2. Other Catalan-like things
3. Higher associativities
4. Higher dimensional foams
Chapter 9. Knots in space
1. Oriented knots and higher categories
2. Reidemeister moves
3. The fundamental group and related invariants
4. The Jones polynomial
5. The braid group
6. More algebraic structures
7. Trivalent graphs
Chapter 10. Foams and surfaces in 4-space
1. Knotted surfaces
2. Foams in 4-space
3. Shalgebras and qualgebras
4. Homology
5. More abstract tensors
6. Conclusion
Chapter 11. Higher dimensional braids
1. Geometric braids
2. Glyphographic description of surface braids
3. Surface braids
4. Charts in 3- and 4-dimensions
5. Conclusion
Chapter 12. Globular multi-categories
1. Arrows and cells
2. Group presentations
3. Conclusion
Bibliography
Index