Sh(B)-Valued Models of (\kappa ,\kappa )-Coherent Categories
| Authors | |
|---|---|
| Year of publication | 2025 |
| Type | Article in Periodical |
| Magazine / Source | Applied Categorical Structures |
| MU Faculty or unit | |
| Citation | |
| web | https://link.springer.com/article/10.1007/s10485-025-09804-4 |
| Doi | http://dx.doi.org/10.1007/s10485-025-09804-4 |
| Keywords | $\kappa $-topos; $\kappa $-site; Method of diagrams; Sh(B)-valued model |
| Description | A basic technique in model theory is to name the elements of a model by introducing new constant symbols. We describe the analogous construction in the language of syntactic categories/sites. As an application we identify Set-valued regular functors on the syntactic category with a certain class of topos-valued models (we will refer to them as "Sh(B)-valued models"). For the coherent fragment L??g?L?? this was proved by Jacob Lurie, our discussion gives a new proof, together with a generalization to L??g when ? is weakly compact. We present some further applications: first, a Sh(B)-valued completeness theorem for L??g (? is weakly compact), second, that C›Set regular functors (on coherent categories with disjoint coproducts) admit an elementary map to a product of coherent functors. |
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