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Computads for Finitary Monads on Globular Sets
, 1998
"... . A finitary monad A on the category of globular sets provides basic algebraic operations from which more involved `pasting' operations can be derived. To makes this rigorous, we define Acomputads and construct a monad on the category of Acomputads whose algebras are Aalgebras; an action of ..."
Abstract

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. A finitary monad A on the category of globular sets provides basic algebraic operations from which more involved `pasting' operations can be derived. To makes this rigorous, we define Acomputads and construct a monad on the category of Acomputads whose algebras are Aalgebras; an action of the new monad encapsulates the pasting operations. When A is the monad whose algebras are ncategories, an Acomputad is an ncomputad in the sense of R.Street. When A is associated to a higher operad (in the sense of the author) , we obtain pasting in weak ncategories. This is intended as a first step towards proving the equivalence of the various definitions of weak ncategory now in the literature. Introduction This work arose as a reflection on the foundation of higher dimensional category theory. One of the main ingredients of any proposed definition of weak ncategory is the shape of diagrams (pasting scheme) we accept to be composable. In a globular approach [3] each kcell has a source ...