The petit topos of globular sets

Ross Street
2000 Journal of Pure and Applied Algebra  
There are now several deÿnitions of weak !-category [1, 2, 5, 19] . What is pleasing is that they are not achieved by ad hoc combinatorics. In particular, the theory of higher operads which underlies Michael Batanin's deÿnition is based on globular sets. The purpose of this paper is to show that many of the concepts of [2] (also see [17] ) arise in the natural development of category theory internal to the petit 1 topos Glob of globular sets. For example, higher spans turn out to be internal
more » ... s, and, in a sense, trees turn out to be internal natural numbers. c 2000 Elsevier Science B.V. All rights reserved. MSC: 18D05 Globular objects and !-categories A globular set is an inÿnite-dimensional graph. To formalize this, let G denote the category whose objects are natural numbers and whose only non-identity arrows are m ; m : m → n for all m ¡ n *
doi:10.1016/s0022-4049(99)00183-8 fatcat:ckpvabdpvzdj5fb2zpl6c35hoa