Abstract
In order to facilitate the study of 2-categories with structure, we state and prove an n-categorical pasting theorem. This is based upon a new definition of n-pasting scheme that generalises Johnson's definition of a well-formed loop-free pasting scheme by weakening his no direct loops condition. We define n-pasting, prove the theorem, and show that for n=3, it incorporates all possible composites of n-cells. We show that that is not true for higher n. We define the horizontal n-category of an (n+1)-category to generalise that of a 2-category, we define horizontal and vertical composition for an (n+1)-category and we state and prove an interchange law. We also study further conditions on a pasting diagram and their impact upon how one may evaluate a composite, and we express Street's free n-categories in terms of left adjoints.
This research was supported by the Australian Research Council and by ESPRIT Basic Research Action 3245: Logical Frameworks Design, Implementation and Experiment.
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dedicated to Max Kelly on the occasion of his 60th birthday.
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© 1991 Springer-Verlag
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Power, A.J. (1991). An n-categorical pasting theorem. In: Carboni, A., Pedicchio, M.C., Rosolini, G. (eds) Category Theory. Lecture Notes in Mathematics, vol 1488. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084230
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DOI: https://doi.org/10.1007/BFb0084230
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