Let (see Segal's category) be the skeleton of the category of finite pointed sets. We write for the finite pointed set with non-basepoint elements. Then a -set is a functor .
The topos of -sets is the classifying topos for pointed objects (MO question). For more on this see also at classifying topos for the theory of objects.
By contrast, in (Connes & Consani 15, 2.1) the authors define a -set to be a pointed functor , the category of pointed sets. The category of -sets in this sense is no longer a topos, but it is a symmetric monoidal closed category. This construction is used in their approach to the field with one element.
Last revised on April 16, 2024 at 13:23:49. See the history of this page for a list of all contributions to it.