Fraïssé’s Construction from a Topos-Theoretic Perspective

Sites whose topoi are the smooth representations of locally prodiscrete monoids

“…Hence the functor C 0,X/ → C ι0(X)/ induced by ι 0 is an equivalence of categories. This shows that that the pair (C 0 , ι 0 ) satisfies property (4), which completes the proof.…”

“…The key input to the proof of the existence of an ultrahomogeneous object of [4,Theorem 2.8] is [4,Lemma 2.7], which is similar to our Lemma 7.7.1. We assume certain cardinality conditions for our lemma, while she restricts to continuous κchains.…”

“…We prove that the pair (C 0 , ι 0 ) satisfies property (3). It remains to be proven that the pair (C 0 , ι 0 ) satisfies property (4). Let X be an object of C 0 .…”

Katětov Functors

“…This has been recently demonstrated by the first author [23], subsequently applied by Caramello [7] in topos theory. It seems that the first work presenting category-theoretic approach to Fraïssé limits is by Droste and Göbel [11] (1989), with applications in algebra and theoretical computer science, simply by considering classes of models with certain restrictions on embeddings.…”

Topologies for intermediate logics

“…For example, the subtopos of a given elementary topos consisting of its double-negation sheaves can be seen as a universal way of making the topos Boolean, as it can be characterized as the largest dense Boolean subtopos of the given topos; similarly, the subtopos of a given elementary topos consisting of its sheaves with respect to the De Morgan topology (as introduced in [2]) can be characterized as its largest dense subtopos satisfying De Morgan's law. These concepts have proved to be fruitful in different contexts (cf., e.g., [7,8]), so it is natural to look for analogues of them for general intermediate logics.…”