The following preprint is available: M. Grandis - R. Paré An introduction to multiple categories (On weak and lax multiple categories, I) Pubbl. Mat. Univ. Genova, Preprint 604 (2015). http://www.dima.unige.it/~grandis/Mlc1.pdf Abstract. Extending double and triple categories, we introduce here infinite dimensional weak multiple categories. We also consider a partially lax, 'chiral' form with directed interchanges and a laxer form already studied in two previous papers for the 3-dimensional case, under the name of intercategory. In these settings we also begin a study of tabulators, the basic higher limits, that will be concluded in a sequel. The two previous papers mentioned above can be found at arXiv: - M. Grandis - R. Paré, Intercategories I: The basic theory. http://arxiv.org/abs/1412.0144 - M. Grandis - R. Paré, Intercategories II: Examples. http://arxiv.org/abs/1412.0212 Marco Grandis and Bob Paré [For admin and other information see: http://www.mta.ca/~cat-dist/ ]