Observing that an anabelioid is in particular a topos, a finite étale morphism of anabelioids is the same as an étale geometric morphism: it is a ‘local isomorphism’, in some sense.
Recall that a morphism of anabelioids? is simply an exact functor , that is to say, a functor preserving both finite limits and finite colimits. The following definition follows Mochizuki2004.
A morphism of anabelioids? is finite étale if there is an object of such that for some isomorphism of anabelioids , where denotes the overcategory of objects of over , and where is the canonical functor.
Last revised on April 17, 2020 at 23:38:49. See the history of this page for a list of all contributions to it.