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**1 - 1**of**1**### Pasting Presentations for Omega-Categories

, 1995

"... The pasting theorem showed that pasting schemes are useful in studying free !-categories. It was thought that their inflexibility with respect to composition and identities prohibited wider use. This is not the case: there is a way of dealing with identities which makes it possible to describe !-ca ..."

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The pasting theorem showed that pasting schemes are useful in studying free !-categories. It was thought that their inflexibility with respect to composition and identities prohibited wider use. This is not the case: there is a way of dealing with identities which makes it possible to describe !-categories in terms of generating pasting schemes and relations between generated pastings, i.e., with pasting presentations. In this chapter I develop the necessary machinery for this. The main result, that the !-category generated by a pasting presentation is universal with respect to respectable families of realizations, is a generalization of the pasting theorem. Contents 1 Introduction 3 2 Pasting schemes according to Johnson 4 2.1 Graded sets : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 4 2.2 !-categories : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 5 2.3 Pasting schemes : : : : : : : : : : : : : : : : : : : : : : : : : : : : 6 2.4 The pasting theorem : : ...