Related papers: Concrete Duality for Strict Infinity Categories
We study concrete sheaf models for a call-by-value higher-order language with recursion. Our family of sheaf models is a generalization of many examples from the literature, such as models for probabilistic and differentiable programming,…
We advocate an account of dualities between physical theories: the basic idea is that dual theories are isomorphic representations of a common core. We defend and illustrate this account, which we call a Schema, in relation to symmetries.…
Dualities are often supposed to be foundational, but they may come into conflict with background independence, because a hidden fixed structures is needed to define the duality transformation. This conflict can be eliminated by extending a…
We construct a canonical extension for strong proximity lattices in order to give an algebraic, point-free description of a finitary duality for stably compact spaces. In this setting not only morphisms, but also objects may have distinct…
In a general triangulated category, the finiteness of the finitistic dimension serves as a prerequisite for a categorical obstruction, via the singularity category, to the existence of bounded $t$-structures. In this paper, we investigate…
We describe a comparison between pretriangulated differential graded categories and certain stable infinity categories. Specifically, we use a model category structure on differential graded categories over k (a field of characteristic 0)…
We consider and characterize classes of finite and countably categorical structures and their theories preserved under $E$-operators and $P$-operators. We describe $e$-spectra and families of finite cardinalities for structures belonging to…
We study the properties of the relative derived category $D_{\mathscr{C}}^{b}$($\mathscr{A}$) of an abelian category $\mathscr{A}$ relative to a full and additive subcategory $\mathscr{C}$. In particular, when $\mathscr{A}=A{\text -}\mod$…
We introduce the class of unshreddable theories, which contains the simple and NIP theories, and prove that such theories have exactly saturated models in singular cardinals, satisfying certain set-theoretic hypotheses. We also give…
We construct a left semi-model category of "marked strict $\infty$-categories" for which the fibrant objects are those whose marked arrows satisfy natural closure properties and are weakly invertible. The canonical model structure on strict…
We consider natural cardinal invariants hm_n and prove several duality theorems, saying roughly: if I is a suitably definable ideal and provably cov(I)>=hm_n, then non(I) is provably small. The proofs integrate the determinacy theory,…
In recent papers and books, a global quantization has been developed for unimodular groups of type I. It involves operator-valued symbols defined on the product between the group $\mathsf{G}$ and its unitary dual $\widehat{\mathsf{G}}$,…
Regular and higher regular graded algebras (in simplest case satisfying Von Neumann regularity $\Theta_{1}\Theta_{2}\Theta_{1}=\Theta_{1}$ instead of anticommutativity) are introduced and their properties are studied. They are described in…
We characterize the generalized Auslander--Reiten duality on the category of finitely presented modules over some certain Hom-finite category. Examples include the category FI of finite sets with injections, and the one VI of finite…
This paper is the second in a series of two papers about generalizing Quillen's Theorem A to strict $\infty$-categories. In the first one, we presented a proof of this Theorem A of a simplicial nature, direct but somewhat ad hoc. In the…
We study the systems of ordinary differential equations which are implicit with respect to the higher derivatives, appearing in the linear form, and their solutions near the singular points. The invertibility of the higher derivatives…
We use type-theoretic techniques to present an algebraic theory of $\infty$-categories with strict units. Starting with a known type-theoretic presentation of fully weak $\infty$-categories, in which terms denote valid operations, we extend…
We define the derived category of a concrete category in a way which extends the usual definition of the derived category of a ring, and we prove that the bounded-below derived category of $\Spec \mathbb{M}_0$ (an approximation, used by…
We classify the module categories over the double (possibly twisted) of a finite group.
In this paper I bring the recent philosophical literature on theoretical equivalence to bear on dualities in physics. Focusing on electromagnetic duality, which is a simple example of S-duality in string theory, I will show that the duality…