#
Stability properties characterising n-permutable categories

##
Pierre-Alain Jacqmin, Diana Rodelo

The purpose of this paper is two-fold. A first and more concrete aim is
to characterise n-permutable categories through certain stability
properties of regular epimorphisms. These characterisations allow us to
recover the ternary terms and the (n+1)-ary terms describing
n-permutable varieties of universal algebras.

A second and more abstract aim is to explain two proof techniques, by
using the above characterisation as an opportunity to provide explicit
new examples of their use:

- an *embedding theorem* for n-permutable categories which allows
us to follow the varietal proof to show that an n-permutable category
has certain properties;

- the theory of *unconditional exactness properties* which allows us
to remove the assumption of the existence of colimits,
in particular when we use the *approximate co-operations* approach
to show that a regular category is n-permutable.

Keywords:
Mal'tsev category, Goursat category, n-permutable category, embedding
theorem, unconditional exactness property

2010 MSC:
08A30, 08B05, 08C05, 18B15, 18B99, 18C99,18A32

*Theory and Applications of Categories,*
Vol. 32, 2017,
No. 45, pp 1563-1587.

Published 2017-12-19.

http://www.tac.mta.ca/tac/volumes/32/45/32-45.pdf

TAC Home