# Questions tagged [semiabelian-categories]

Semiabelian categories are pointed exact protomodular categories with coproducts. Suitable for questions about protomodular categories as well.

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### Give examples of semi-abelian schemes over a curve

Let $C$ be a nice curve, i.e. $C$ is a smooth, projective, geometrically integral scheme of dimension $1$ over a field $k$. For example, (assuming the characteristic of $k$ is neither 2 or 3)an ...

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### Is the category of racks semi-abelian?

I wonder whether the category of (pointed) racks is semi-abelian.
Any comments and references would be appreciated.

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### Relating three viewpoints on the semidirect product

It's known that giving a semidirect product $(X,m)\rtimes G$ of a $G$-group $(X,m)$ with $G$ (as defined in wiki) is the same as giving a split pair over $G$, i.e a pair of arrows $H\overset{s}{\...