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We compare computads with multitopic sets. Both these kinds of structures have n-dimensional objects (called n-cells and n-pasting diagrams, respectively). The computads form a subclass of the more familiar class of omega-categories, while multitopic sets have been devised by Hermida, Makkai and Power as a vehicle for a definition of the concepts of weak omega-category. Our main result states that the category of multitopic sets is equivalent to that of many-to-one computads, a certain full subcategory of the category of all computads.
We define a general notion of centrally $Gamma$-graded sets and groups and of their graded products, and prove some basic results about the corresponding categories: most importantly, they form braided monoidal categories. Here, $Gamma$ is an arbitra
Many special classes of simplicial sets, such as the nerves of categories or groupoids, the 2-Segal sets of Dyckerhoff and Kapranov, and the (discrete) decomposition spaces of G{a}lvez, Kock, and Tonks, are characterized by the property of sending ce
In The factorization of the Giry monad (arXiv:1707.00488v2) the author considers two $sigma$-algebras on convex spaces of functions to the unit interval. One of them is generated by the Boolean subobjects and the other is the $sigma$-algebra induced
We define a general concept of pseudo algebras over theories and 2-theories. A more restrictive such notion was introduced by Hu and Kriz, but as noticed by M. Gould, did not capture the desired examples. The approach taken in this paper corrects the
We describe an abstract 2-categorical setting to study various notions of polynomial and analytic functors and monads.