Contents

1 Introduction

2 Categories

3 Monoidal categories
3.1 (Planar) monoidal categories
3.2 Spacial monoidal categories
3.3 Braided monoidal categories
3.4 Balanced monoidal categories
3.5 Symmetric monoidal categories

4 Autonomous categories
4.1 (Planar) autonomous categories
4.2 (Planar) pivotal categories
4.3 Spherical pivotal categories
4.4 Spacial pivotal categories
4.5 Braided autonomous categories
4.6 Braided pivotal categories
4.7 Tortile categories
4.8 Compact closed categories

5 Traced categories
5.1 Right traced categories
5.2 Planar traced categories
5.3 Spherical traced categories
5.4 Spacial traced categories
5.5 Braided traced categories
5.6 Balanced traced categories
5.7 Symmetric traced categories

6 Products, coproducts, and biproducts
6.1 Products
6.2 Coproducts
6.3 Biproducts
6.4 Traced product, coproduct, and biproduct categories
6.5 Uniformity and regular trees
6.6 Cartesian center

7 Dagger categories
7.1 Dagger monoidal categories
7.2 Other progressive dagger monoidal notions
7.3 Dagger pivotal categories
7.4 Other dagger pivotal notions
7.5 Dagger traced categories
7.6 Dagger biproducts

8 Bicategories

9 Beyond a single tensor product

10 Summary