Related papers: Every theory is eventually of presheaf type
We give a new description of computads for weak globular $\omega$-categories by giving an explicit inductive definition of the free words. This yields a new understanding of computads, and allows a new definition of $\omega$-category that…
Represented spaces form the general setting for the study of computability derived from Turing machines. As such, they are the basic entities for endeavors such as computable analysis or computable measure theory. The theory of represented…
This is the third installment in a series of papers on algebraic set theory. In it, we develop a uniform approach to sheaf models of constructive set theories based on ideas from categorical logic. The key notion is that of a "predicative…
This paper provides a preparatory introduction to sheaves and topoi, written as a conceptual continuation of the author's earlier introduction to torsors and as preparatory background for the author's arXiv paper \emph{Grothendieck…
In Proposition I of "Memoire sur les conditions de resolubilite des equations par radicaux", Galois established that any intermediate extension of the splitting field of a polynomial with rational coefficients is the fixed field of its…
In this paper we introduce primigraph spaces, which are topological spaces together with a sheaf of $C^*$-algebras that can be covered by some Prim A's, that is, by the primitive spectra of some $C^*$-algebras endowed with Jacobson topology…
We give an explicit construction of the category Opetope of opetopes. We prove that the category of opetopic sets is equivalent to the category of presheaves over Opetope.
In this paper, we prove that if $\kappa$ is a almost strongly compact cardinal, then any MAEC with L\"owenheim-Skolem number below $\kappa$ is $<\kappa$-d-tame.
We study relative precompleteness in the context of the theory of numberings, and relate this to a notion of lowness. We introduce a notion of divisibility for numberings, and use it to show that for the class of divisible numberings,…
We prove a fixed point theorem for closed-graphed, decomposable-valued correspondences whose domain and range is a decomposable set of functions from an atomless measure space to a topological space. One consequence is an improvement of the…
For a given $\omega$-operad $A$ on globular sets we introduce a sequence of symmetric operads on $Set$ called slices of $A$ and show how the connected limit preserving properties of slices are related to the property of the category of…
New fixed point results are presented for ${\cal U}_c^{\kappa}(X,X)$ maps in extension type spaces.
We generalise sheaf models of intuitionistic logic to univalent type theory over a small category with a Grothendieck topology. We use in a crucial way that we have constructive models of univalence, that can then be relativized to any…
In this article, the theory of sheaves is studied from a categorical point of view. This perspective vastly generalizes the usual theory of sheaves of sets to a more abstract setting which allows us to investigate the theory of sheaves with…
In [EH89, Theorem 1] Ekeland-Hofer prove that for a centrally symmetric, restricted contact type hypersurface in R^{2n} and for any global, centrally symmetric Hamiltonian perturbation there exists a leaf-wise intersection point. In this…
We prove a model theoretic Baire category theorem for $\tilde\tau_{low}^f$-sets in a countable simple theory in which the extension property is first-order and show some of its applications. We also prove a trichotomy for minimal types in…
In this paper, we develop an Isabelle/HOL library of order-theoretic fixed-point theorems. We keep our formalization as general as possible: we reprove several well-known results about complete orders, often with only antisymmetry or…
The goal of this paper is to summarise the first steps in developing a fundamentally new way of constructing theories of physics. The motivation comes from a desire to address certain deep issues that arise when contemplating quantum…
The first part of this dissertation defines "dependently typed algebraic theories", which are a strict subclass of the generalised algebraic theories (GATs) of Cartmell. We characterise dependently typed algebraic theories as finitary…
Main Result: Let $(M,L)$ be a smooth complex polarized threefold. Then the linear system $| K+tL|$ separates any two different points on $M$ for any $t\ge 6$, where $K$ is the canonical bundle of $M$. The argument in the proof is a variant…