Abstract Clones and Operads |
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Authors: | Tronin S N |
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Institution: | (1) Kazan' State University, Kazan' |
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Abstract: | We establish a connection between abstract clones and operads, which implies that both clones and operads are particular instances of a more general notion. The latter is called W-operad (due to a close resemblance with operads) and can be regarded as a functor on a certain subcategory W, of the category of finite ordinals, with some rather natural properties. When W is a category whose morphisms are the various bijections, the variety of W-operads is rationally equivalent to the variety of operads in the traditional sense. Our main result claims that if W coincides with the category of all finite ordinals then the variety of W-operads is rationally equivalent to the variety of abstract clones. |
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Keywords: | operad abstract clone variety rational equivalence |
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