Extended Graphical Calculus for Categorified Quantum sl(2).

Intro -- Contents -- Abstract -- Chapter 1. Introduction -- 1.1. The algebra -- 1.2. Categorification -- 1.3. Diagrammatics for the Karoubi envelope -- 1.4. Categorification and symmetric functions -- 1.5. Relations to other categorifications -- Chapter 2. Thick calculus for the nilHecke ring -- 2.1. The nilHecke ring and its diagrammatics -- 2.2. Boxes, thick lines, and splitters -- 2.3. Partitions, symmetric functions, and their diagrammatics -- 2.4. Splitter equations, explosions, and idempotents -- 2.5. The nilHecke algebra as a matrix algebra over its center -- Chapter 3. Brief review of calculus for categorified sl(2) -- 3.1. The algebra -- 3.2. The 2-category -- 3.3. Box notation for -- 3.4. Karoubi envelope -- Chapter 4. Thick calculus and -- 4.1. Thick lines oriented up or down -- 4.2. Splitters as diagrams for the inclusion of a summand -- 4.3. Adding isotopies via thick caps and cups -- 4.4. Thin bubble slides -- 4.5. Thick bubbles -- 4.6. Thick bubble slides and some key lemmas -- Chapter 5. Decompositions of functors and other applications -- 5.1. Decomposition of ℰ^{( )}ℰ^{( )}1_{ } -- 5.2. Decomposition of ℰ^{( )}ℱ^{( )}1_{ } -- 5.3. Indecomposables over ℤ -- 5.4. Bases for HOMs between some 1-morphisms -- Bibliography.

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