## You are here

HomeVan Kampen's theorem result

## Primary tabs

# Van Kampen's theorem result

The Van Kampen's theorem for groupoids as stated in this entry is incomplete:

``{\bf Theorem} If $X$ is the union of open sets $U,V$ with intersection $W$,

and $A$ meets each path component of $U,V,W$ then the following induced diagram

$$\xymatrix{ \pi_1(W,A) \ar [r] \ar [d] & \pi_1(U,A) \ar [d] \\

\pi_1(V,A) \ar [r] & \pi_1(X,A)} $$

is a pushout in the category of groupoids."

, whereas the remark in this entry about the Van Kampen's theorem for groups is relevant to the former and should be kept.

The statement of the Van Kampen's theorem for groupoids in this entry, therefore, should be simply referring to the existing, correct entry at PM by using the {\bf Related} entry function of the PM's old Noosphere linking it to the Object id 3947, with the canonical name of `` VanKampensTheorem "; otherwise it is inconsistent with the correct statement of this theorem as completelely presented in the object with the id 3947,

**Status:**Waiting for response

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff
- Corrections