%0 Report %1 schneider:2009 %A Schneider, Friedrich Martin %D 2009 %K 2009 preprint schneider %N MATH-AL-03-2009 %T Weak Homomorphisms between Functorial Algebras %X In the theory of universal algebras homomorphisms are considered only between algebras of the same similarity type. Different from that, the notion of a weak homomorphism does not depend on a signature, but only on the clones of term operations generated by the examined algebras. We generalize this idea by defining weak homomorphisms between $F_1$- and $F_2$-algebras, where $F_1$ and $F_2$ denote not necessarily equal endofunctors of the category of sets. The aim is to prove useful properties of weak homomorphisms which correspond to some well-known results for usual homomorphisms.

@techreport{schneider:2009, abstract = {In the theory of universal algebras homomorphisms are considered only between algebras of the same similarity type. Different from that, the notion of a weak homomorphism does not depend on a signature, but only on the clones of term operations generated by the examined algebras. We generalize this idea by defining weak homomorphisms between $F_{1}$- and $F_{2}$-algebras, where $F_{1}$ and $F_{2}$ denote not necessarily equal endofunctors of the category of sets. The aim is to prove useful properties of weak homomorphisms which correspond to some well-known results for usual homomorphisms. }, added-at = {2010-05-10T09:53:35.000+0200}, author = {Schneider, Friedrich Martin}, biburl = {https://www.bibsonomy.org/bibtex/2c6a9edc536fb53b0483eed63781f2fde/algebradresden}, institution = {TU Dresden}, interhash = {9855eda7bc5862766bfe4919196845e9}, intrahash = {c6a9edc536fb53b0483eed63781f2fde}, keywords = {2009 preprint schneider}, month = dec, number = {MATH-AL-03-2009}, timestamp = {2010-05-10T09:53:35.000+0200}, title = {Weak Homomorphisms between Functorial Algebras}, year = 2009 }