In the context of regular unital categories we introduce an intrinsic version of the notion of a Schreier split epimorphism , originally considered for monoids. We show that such split epimorphisms satisfy the same homological properties as Schreier split epimorphisms of monoids do. This gives rise to new examples of $${\mathcal {S}}$$ S -protomodular categories, and allows us to better understand the homological behaviour of monoids from a categorical perspective.

中文翻译：

---

内在 Schreier 拆分扩展

在常规单位范畴的上下文中，我们引入了 Schreier 分裂表同态的概念的内在版本，最初考虑用于幺半群。我们表明，这种分裂表同满足与幺半群的 Schreier 分裂表态相同的同调性质。这产生了 $${\mathcal {S}}$$ S -protomodular 范畴的新例子，并使我们能够从范畴的角度更好地理解幺半群的同调行为。