Reading Group 101

General Information

A small collection of Definitions and examples we encountered during our reading group. It is neither complete nor especially proofread, but hopefully provides some overview of what we discuss and if there are holes we want to close :)

Most Important Definitions

Categories

A category is a:

• Collection of objects: $A$, $B$, $C$ etc.
• A collections of morphisms: $f$, $g$, …
  • for every objects there exists an identity morphism $1_a$
  • Morphisms may compose if domain and codomain match.

$$\begin{array}{ccc}K(X)& \stackrel{ch}{\to }& H(X;\mathbb{Q});\\ \downarrow & & \downarrow \\ K(Y)& \stackrel{ch}{\to }& H(Y;\mathbb{Q});\end{array}$$