3
$\begingroup$

Consider $\mathbb{G}$, which can be viewed as a group, as well as a 2-group.

(For example, given a short exact sequence $$ 1 \to BG_2 \to \mathbb{G} \to G_1 \to 1 $$ and the fiber sequence: $$ B^2G_2 \to B\mathbb{G} \to BG_1. $$ where $\mathbb{G}$ can be viewed as a group or a 2-group.)

The consideration is the following:

$$G \text{ has one object}.$$

$$BG \text{ has one 0-cell}.$$

$$1\text{-morphisms} = \text{ elements of } \mathbb{G}.$$

$$1\text{-cells} = 1\text{-morphisms of } \mathbb{G}.$$

  • Question: What is the precise relation between the cell structure on $B\mathbb{G}$ and the bar resolution of $\mathbb{G}$?

Thank you in advance for your help, comments, answers!

$\endgroup$

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.