Related papers: Extensional concepts in intensional type theory, r…
In generic realizability for set theories, realizers treat unbounded quantifiers generically. To this form of realizability, we add another layer of extensionality by requiring that realizers ought to act extensionally on realizers, giving…
We prove that every categorical model of dependent type theory with dependent sums and products, intensional identity types and univalent universes presents via its $\infty$-localisation an elementary $\infty$-topos, that is, a finitely…
In the present paper, we introduce a multibasic extension of the Ehrhart theory. We give a multibasic extension of Ehrhart polynomials and Ehrhart series. We also show that an analogue of Ehrhart reciprocity holds for multibasic Ehrhart…
We construct a symmetric monoidal closed category of polynomial endofunctors (as objects) and simulation cells (as morphisms). This structure is defined using universal properties without reference to representing polynomial diagrams and is…
We introduce a calculus of extensional resource terms. These are resource terms \`a la Ehrhard-Regnier, but in infinitely eta-long form. The calculus still retains a finite syntax and dynamics: in particular, we prove strong confluence and…
We study two notions of definability for classes of relational structures based on modal extensions of {\L}ukasiewicz finitely valued-logics. The main results of the paper are the equivalent of the Goldblatt - Thomason theorem for these…
We introduce Morita equivalence for Nijenhuis groupoids and for their infinitesimal counterparts, establishing a global-to-infinitesimal correspondence under the Lie functor. A special case is that of holomorphic Lie groupoids and…
A notion of a coring extension is defined and it is related to the existence of an additive functor between comodule categories that factorises through forgetful functors. This correspondence between coring extensions and factorisable…
We define a notion of colimit for diagrams in a motivic category indexed by a presheaf of spaces (e.g. an \'etale classifying space), and we study basic properties of this construction. As a case study, we construct the motivic analogs of…
In this work we provide alternative formulations of the concepts of lambda theory and extensional theory without introducing the notion of substitution and the sets of all, free and bound variables occurring in a term. We also clarify the…
The following strong form of density of definable types is introduced for theories T admitting a fibered dimension function d: given a model M of T and a definable subset X of M^n, there is a definable type p in X, definable over a code for…
For a relational Horn theory $\mathbb{T}$, we provide useful sufficient conditions for the exponentiability of objects and morphisms in the category $\mathbb{T}\text{-}\mathsf{Mod}$ of $\mathbb{T}$-models; well-known examples of such…
We improve the exodromy equivalence of MacPherson, Treumann and Lurie in several ways: first, we allow stratified spaces that have locally weakly contractible strata, rather than being locally of singular shape, we remove all noetherianity…
A standard intensional account of probabilistic computation represents a randomized program as a deterministic computation that consumes an explicit random tape. This yields a two-layer perspective: an intensional layer that makes reuse of…
Motivated by representation theory and geometry, we introduce and develop an equivariant generalization of Ehrhart theory, the study of lattice points in dilations of lattice polytopes. We prove representation-theoretic analogues of…
The usual homogeneous form of equality type in Martin-L\"of Type Theory contains identifications between elements of the same type. By contrast, the heterogeneous form of equality contains identifications between elements of possibly…
In this note, we investigate iterations of consistency, local and uniform reflection over $\mathbf{HA}$ (Heyting Arithmetic). In the case of uniform reflection, we give a new proof of Dragalin's extension of Feferman's completeness theorem…
We consider model-theoretic properties related to the expressive power of three analogues of $L_{\omega_1, \omega}$ for metric structures. We give an example showing that one of these infinitary logics is strictly more expressive than the…
We study upper bounds, approximations, and limits for functions of motivic exponential class, uniformly in non-Archimedean local fields whose characteristic is $0$ or sufficiently large. Our results together form a flexible framework for…
By combining classical techniques together with two novel asymptotic identities contained in [FL], we analyse certain single sums of Riemann-zeta type. In addition, we analyse Euler-Zagier double exponential sums for particular values of…