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.
Keywords: snail lemma, snake lemma, protomodular category, strong homotopy kernel
2010 MSC: 18G50, 18D05, 18G55
Theory and Applications of Categories, Vol. 31, 2016, No. 19, pp 484-501.