Thesaurus racks: Categorizing rack objects
Abstract
We define and explore rack objects internal to categories with products. In demonstration, we classify the group-racks, and use homotopy to prove both existence and exclusion theorems for path-connected topological racks.
The Rack Roll (Mel: Rick Astley — Never Gonna Give You Up) We’re no strangers to knots, You know the rules, and so do I. A faithful functor’s what I’m thinking of; You wouldn’t get this x from any other y. I just want to tell you ’bout the quandle; Gonna make you understand:
For every single Abelian cat, every single formal rack, doesn’t really matter what; there’s a quandle. For every single pointed space, every time you choose a base, whenever you compute a trace; there’s a quandle.
In the beginning there was knotting, then Joyce shed light upon what was and was not knot; his fundamental quandle classifying whether a new knot’s the same as what you’ve got. And if you ask any topologist, they’ll say they read Joyce and rejoiced.
