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Hi, Recently I've been looking at the more general version of Van Kampen's theorem, or R. Browns version of it, for the fundamental groupoid. It mentions that if a space X is the union of the interiors of $X_1$ and $X_2$ , then:

![alt text][1]alt text

is a pushout in the category of groupoids. In the category of groups, we have the concrete description that the pushout is just the free product with amalgation. Does something similar hold here? Is there any explicit description, like free product with amalgation? [1]: https://upload.wikimedia.org/wikipedia/commons/thumb/9/91/SeifertvanKampenPO.PNG/244px-SeifertvanKampenPO.PNG

Hi, Recently I've been looking at the more general version of Van Kampen's theorem, or R. Browns version of it, for the fundamental groupoid. It mentions that if a space X is the union of the interiors of $X_1$ and $X_2$ , then:

![alt text][1]

is a pushout in the category of groupoids. In the category of groups, we have the concrete description that the pushout is just the free product with amalgation. Does something similar hold here? Is there any explicit description, like free product with amalgation? [1]: https://upload.wikimedia.org/wikipedia/commons/thumb/9/91/SeifertvanKampenPO.PNG/244px-SeifertvanKampenPO.PNG

Hi, Recently I've been looking at the more general version of Van Kampen's theorem, or R. Browns version of it, for the fundamental groupoid. It mentions that if a space X is the union of the interiors of $X_1$ and $X_2$ , then:

alt text

is a pushout in the category of groupoids. In the category of groups, we have the concrete description that the pushout is just the free product with amalgation. Does something similar hold here? Is there any explicit description, like free product with amalgation?

replaced http://upload.wikimedia.org/ with https://upload.wikimedia.org/
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Hi, Recently I've been looking at the more general version of Van Kampen's theorem, or R. Browns version of it, for the fundamental groupoid. It mentions that if a space X is the union of the interiors of $X_1$ and $X_2$ , then:

![alt text][1]

is a pushout in the category of groupoids. In the category of groups, we have the concrete description that the pushout is just the free product with amalgation. Does something similar hold here? Is there any explicit description, like free product with amalgation? [1]: http://upload.wikimedia.org/wikipedia/commons/thumb/9/91/SeifertvanKampenPO.PNG/244px-SeifertvanKampenPO.PNGhttps://upload.wikimedia.org/wikipedia/commons/thumb/9/91/SeifertvanKampenPO.PNG/244px-SeifertvanKampenPO.PNG

Hi, Recently I've been looking at the more general version of Van Kampen's theorem, or R. Browns version of it, for the fundamental groupoid. It mentions that if a space X is the union of the interiors of $X_1$ and $X_2$ , then:

![alt text][1]

is a pushout in the category of groupoids. In the category of groups, we have the concrete description that the pushout is just the free product with amalgation. Does something similar hold here? Is there any explicit description, like free product with amalgation? [1]: http://upload.wikimedia.org/wikipedia/commons/thumb/9/91/SeifertvanKampenPO.PNG/244px-SeifertvanKampenPO.PNG

Hi, Recently I've been looking at the more general version of Van Kampen's theorem, or R. Browns version of it, for the fundamental groupoid. It mentions that if a space X is the union of the interiors of $X_1$ and $X_2$ , then:

![alt text][1]

is a pushout in the category of groupoids. In the category of groups, we have the concrete description that the pushout is just the free product with amalgation. Does something similar hold here? Is there any explicit description, like free product with amalgation? [1]: https://upload.wikimedia.org/wikipedia/commons/thumb/9/91/SeifertvanKampenPO.PNG/244px-SeifertvanKampenPO.PNG

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The fundamental groupoid and a pushout in the category of groupoids.

Hi, Recently I've been looking at the more general version of Van Kampen's theorem, or R. Browns version of it, for the fundamental groupoid. It mentions that if a space X is the union of the interiors of $X_1$ and $X_2$ , then:

![alt text][1]

is a pushout in the category of groupoids. In the category of groups, we have the concrete description that the pushout is just the free product with amalgation. Does something similar hold here? Is there any explicit description, like free product with amalgation? [1]: http://upload.wikimedia.org/wikipedia/commons/thumb/9/91/SeifertvanKampenPO.PNG/244px-SeifertvanKampenPO.PNG