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Through abelian categories, homological lemmas for modules admit a self-dualtreatment, where half of the proof of a lemma is sufficient to prove the fulllemma. In this paper, we show how the context of a `noetherian form', recentlyintroduced by the second and third authors, allows a self-dual treatment ofthese lemmas even in the case of non-abelian categories of group-likestructures. This context covers a wide range of examples: module categories,the category of groups, of graded abelian groups, the categories of Liealgebras, of cocommutative Hopf algebras, the category of Heyting semilattices,of loops, the dual of the category of pointed sets, the category ofmodular/distributive lattices and modular connections, the category of sets andpartial bijections, and many others. More generally, it includes allsemi-abelian and Grandis exact categories.

Homological lemmas for (non-abelian) group-like structures by diagram chasing in a self-dual context