Paper Info
Title
Dualizing Clones as Models of Lawvere Theories
Abstract
While universal algebraists are well aware of the equivalence between abstract clones and Lawvere theories as well as that of concrete clones and models of Lawvere theories in the category of sets, they almost never use the category-theoretic framework. It seems as if they simply do not see a reason why it might be beneficial to use category theory in order to study the problems that they are interested in. In this paper, we argue that the possibility of applying duality theory might be such a reason, and we support this claim by outlining how treating and dualizing clones as models of Lawvere theories can be beneficial for the classical problem of studying the lattice of clones on a given set. In particular, we give several examples of concrete results that are obtained with this method.
Year
DOI
Venue
2014
10.1016/j.entcs.2014.02.005
Electr. Notes Theor. Comput. Sci.
Keywords
Field
DocType
lawvere theories,lawvere theory,concrete clone,category theory,dualizing clone,concrete result,dualizing clones,universal algebraists,duality theory,classical problem,category-theoretic framework,abstract clone,clones
Discrete mathematics,Lattice (order),Duality (mathematics),Equivalence (measure theory),Category theory,Category of sets,Mathematics
Journal
Volume
ISSN
Citations 
303,
1571-0661
3
PageRank 
References 
Authors
0.45
3
1
Name
Order
Citations
PageRank
Sebastian Kerkhoff1225.93