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Keywords:
Cyclic category; duplicial category; orbit category; 2-group; crossed module; slice 2-category
Cyclic category; duplicial category; orbit category; 2-group; crossed module; slice 2-category
Summary:
The self-duality of the paracyclic category is extended to the homotopy categories of a certain class of (2,1)-categories. These generalise the orbit category of a group and are associated to suitable self-dual preorders equipped with a presheaf of groups and a cosieve. The slice 2-category of equidimensional submanifolds of a compact manifold without boundary is a particular case, and for $S^1$, one recovers cyclic duality. This provides in particular a visualisation of the results of Böhm and Ştefan on the topic.
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