Related papers: Toward the effective 2-topos

We propose to use orthologic as the basis for designing type systems supporting intersection, union, and negation types in the presence of subtyping assumptions. We show how to extend orthologic to support monotonic and antimonotonic…

We present an abstract unifying framework for interpreting Stone-type dualities; several known dualities are seen to be instances of just one topos-theoretic phenomenon, and new dualities are introduced. In fact, infinitely many new…

In this article we prove that multidimensional effective S-adic systems, obtained by applying an effective sequence of substitutions chosen among a finite set of substitutions, are sofic subshifts.

We introduce judgemental theories and their calculi as a general framework to present and study deductive systems. As an exemplification of their expressivity, we approach dependent type theory and natural deduction as special kinds of…

The explicit expression of all the WZW effective actions for a simple group G broken down to a subgroup H is established in a simple and direct way, and the formal similarity of these actions to the Chern-Simons forms is explained.…

We show that the category of truncated spaces with finite homotopy invariants ($\pi$\=/finite spaces) has many of the features expected of an elementary \oo topos. It should be thought of as the natural higher analogue of the elementary…

A paratopological group $G$ has a {\it suitable set} $S$. The latter means that $S$ is a discrete subspace of $G$, $S\cup \{e\}$ is closed, and the subgroup $\langle S\rangle$ of $G$ generated by $S$ is dense in $G$. Suitable sets in…

We survey some results on toric topology.

A generalization of topos theory is proposed giving an abstract realization of such categories as, say, the categories of manifolds and of Grothendieck schemes on the one hand, and permitting one, on the other hand, a view on…

We show that the category of log homotopy types is a full subcategory of a category of homotopy types with modulus.

We present a criterion for $2$-final $(2,1)$-functors, analoguous to the classical one for final $1$-functor: a $(2,1)$-functor $F \colon A \to B$ is $2$-final if and only if, for any object $b$ of $B$, the slice $(2,1)$-category $b / F$ is…

We build a concrete and natural model for the strict 2-category of orbifolds. In particular we prove that if one localizes the 2-category of proper etale Lie groupoids at a class of 1-arrows that we call "covers", then the strict 2-category…

We have generalised the notion of categorical theory in model theory to the context of coherent theories. We prove a duality result between the full sub-2-category of pretopoi which are categorical, and the 2-category of profinite monoids.…

This paper gives a uniform-theoretic refinement of classical homotopy theory. Both cubical sets (with connections) and uniform spaces admit classes of weak equivalences, special cases of classical weak equivalences, appropriate for the…

We determine the groups which can appear as the normalizer of a maximal torus in a connected 2-compact group. The technique depends on using ideas of Tits to give a novel description of the normalizer of the torus in a connected compact Lie…

We show that the category of graphs has the structure of a 2-category with homotopy as the 2-cells. We then develop an explicit description of homotopies for finite graphs, in terms of what we call `spider moves'. We then create a category…

We use Kan injectivity to axiomatise concepts in the 2-category of topoi. We showcase the expressivity of this language through many examples, and we establish some aspects of the formal theory of Kan extension in this 2-category (pointwise…

We study toposes of actions of monoids on sets. We begin with ordinary actions, producing a class of presheaf toposes which we characterize. As groundwork for considering topological monoids, we branch out into a study of supercompactly…

We provide new results on the existence of nonzero positive weak solutions for a class of second order elliptic systems. Our approach relies on a combined use of iterative techniques and classical fixed point index. Some examples are…

We deal with (< kappa)-supported iterated forcing notions which are (E_0,E_1)-complete, have in mind problems on Whitehead groups, uniformizations and the general problem. We deal mainly with the successor of a singular case. This continues…