For a general description of homomorphisms, we refer to Chapter MAPPINGS. This section describes some special aspects of homomorphisms whose domain is a rewrite monoid.
Monoids in the category MonRWS currently are accepted as codomains only for monoid homomorphisms, whose codomain is a rewrite monoid as well.
Returns the homomorphism from the rewrite group M to the monoid N defined by the expression S which must be the one of the following:It is the user's responsibility to ensure that the provided generator images actually give rise to a well-defined homomorphism. No checking is performed by the constructor. Presently, N must be either a rewrite monoid or a group, and it is not possible to define a homomorphism by assigning images to the elements of an arbitrary generating set of M.
- (i)
- A list, sequence or indexed set containing the images of the n generators M.1, ..., M.n of M. Here, the i-th element of S is interpreted as the image of M.i, i.e. the order of the elements in S is important.
- (ii)
- A list, sequence, enumerated set or indexed set, containing n tuples <xi, yi> or arrow pairs xi - > yi, where xi is a generator of M and yi∈N (i=1, ..., n) and the set {x1, ..., xn} is the full set of generators of M. In this case, yi is assigned as the image of xi, hence the order of the elements in S is not important.