Related papers: A study of Kock's fat Delta

A new class of locally unital and locally finite dimensional algebras $A$ over an arbitrary algebraically closed field is discovered. Each of them admits an upper finite weakly triangular decomposition, a generalization of an upper finite…

This paper explores the relationship amongst the various simplicial and pseudo-simplicial objects characteristically associated to any bicategory C. It proves the fact that the geometric realizations of all of these possible candidate…

We report a non-trivial feature of the vacuum structure of free massive or massless Dirac fields in the hyperbolic de Sitter spacetime. Here we have two causally disconnected regions, say $R$ and $L$ separated by another region, $C$. We are…

This paper contains results from two areas -- formal theory of Kan extensions and concrete categories. The contribution to the former topic is based on the extension of the concept of Kan extension to the cones and we prove that limiting…

In this paper, we study the notion of smooth $\infty$-categories within the framework of a six-functor formalism. By leveraging the theory of condensed mathematics and analytic stacks, we apply these results to demonstrate that a rigid…

We show that contrary to appearances, Multimodal Type Theory (MTT) over a 2-category M can be interpreted in any M-shaped diagram of categories having, and functors preserving, M-sized limits, without the need for extra left adjoints. This…

Starting from a (small) rigid C$^*$-tensor category $\mathscr{C}$ with simple unit, we construct von Neumann algebras associated to each of its objects. These algebras are factors and can be either semifinite (of type II$_1$ or II$_\infty$,…

Inspired by the work of Bell on the dynamical Mordell-Lang conjecture, and by family Floer cohomology, we construct p-adic analytic families of bimodules on the Fukaya category of a monotone or negatively monotone symplectic manifold,…

The representation theory of finite groups began with Frobenius's factorization of Dedekind's group determinant. In this paper, we consider the case of the semigroup determinant. The semigroup determinant is nonzero if and only if the…

Many definitions of weak and strict $\infty$-categories have been proposed. In this paper we present a definition for $\infty$-categories with strict associators, but which is otherwise fully weak. Our approach is based on the existing type…

We introduce a method to lift monads on the base category of a fibration to its total category. This method, which we call codensity lifting, is applicable to various fibrations which were not supported by its precursor, categorical…

Let $G$ be a semisimple simply-connected algebraic group over an algebraically closed field of characteristic zero. We prove that the affine Hecke category associated to the loop group of $G$ is equivalent to the colimit, evaluated in the…

In this article we revisit the partial Selmer groups introduced by Ding in cohomological degree one. On the subcategory of partially de Rham positive $B$-pairs we extend them to higher cohomological degree and show that the resulting groups…

This thesis is about trying to understand various aspects of partial symmetry using ideas from semigroup and category theory. In Chapter 2 it is shown that the left Rees monoids underlying self-similar group actions are precisely monoid…

We construct a group associated to a class of Borcherds algebras that admit a direct sum decomposition into a Kac--Moody (or semi-simple) subalgebra and a pair of free Lie subalgebras. Such Borcherds algebras have no mutually orthogonal…

We present a simple functional integration based proof that the semigroups generated by the ultraviolet-renormalized translation-invariant non- and semi-relativistic Nelson Hamiltonians are positivity improving (and hence ergodic) with…

We use the basic expected properties of the Gray tensor product of $(\infty,2)$-categories to study (co)lax natural transformations. Using results of Riehl-Verity and Zaganidis we identify lax transformations between adjunctions and monads…

We present a conservative extension ICaTT of the dependent type theory CaTT for weak $\omega$-categories with a type witnessing coinductive invertibility of cells. This extension allows for a concise description of the "walking equivalence"…

We introduce rigid algebras, a generalization of rigid categories to arbitrary symmetric monoidal $(\infty,2)$-categories. We develop their general theory, showing in particular that the a priori $(\infty,2)$-category of rigid algebras is…

Every countable directed graph generates a Fock space Hilbert space and a family of partial isometries. These operators also arise from the left regular representations of free semigroupoids derived from directed graphs. We develop a…