• Corpus ID: 115168067

Internal object actions in homological categories

  title={Internal object actions in homological categories},
  author={Manfred Hartl and Bruno Loiseau},
  journal={arXiv: Category Theory},
Let $G$ and $A$ be objects of a finitely cocomplete homological category $\mathbb C$. We define a notion of an (internal) action of $G$ of $A$ which is functorially equivalent with a point in $\mathbb C$ over $G$, i.e. a split extension in $\mathbb C$ with kernel $A$ and cokernel $G$. This notion and its study are based on a preliminary investigation of cross-effects of functors in a general categorical context. These also allow us to define higher categorical commutators. We show that any… 
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