The snail lemma

Vitale, Enrico
(2016) Theory and Applications of Categories — Vol. 31, n° 19, p. 484-501 (2016)

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Abstract
The classical snake lemma produces a six terms exact sequence starting from a commutative square with one of the edge being a regular epimorphism. We establish a new diagram lemma, that we call snail lemma, removing such a condition. We also show that the snail lemma subsumes the snake lemma and we give an interpretation of the snail lemma in terms of strong homotopy kernels. Our results hold in any pointed regular protomodular category.
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Vitale, E. (2016). The snail lemma. Theory and Applications of Categories, 31(19), 484-501. https://hdl.handle.net/2078.5/182959 (Original work published 2016)