# The snail lemma

• Published in 2016
In the collections
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.

### BibTeX entry

@article{Thesnaillemma,
title = {The snail lemma},
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.},
url = {http://www.tac.mta.ca/tac/volumes/31/19/31-19abs.html http://www.tac.mta.ca/tac/volumes/31/19/31-19.pdf},
author = {Enrico M. Vitale},
comment = {},
urldate = {2016-06-13},
collections = {Attention-grabbing titles,Animals},
year = 2016
}