Related papers: Weak cartesian properties of simplicial sets
A weakly complete space is a complex space admitting a (smooth) plurisubharmonic exhaustion function. In this paper, we classify those weakly complete complex surfaces for which such exhaustion function can be chosen real analytic: they can…
In a recent paper we introduced a much weaker and easy to verify structure than a model category, which we called a "weak fibration category". We further showed that a small weak fibration category can be "completed" into a full model…
In this paper, we propose a mild condition, named Condition $(**)$, for collections of sequence of integers and show that for any measure preserving system the Pinsker $\sigma$-algebra is a characteristic $\sigma$-algebra for the averages…
Let $\Delta$ be an (abstract) simplicial complex on $n$ vertices. One can define the Artinian monomial algebra $A(\Delta) = \Bbbk[x_1, \ldots, x_n]/ \langle x_1^2, \ldots, x_n^2, I_{\Delta} \rangle$, where $\Bbbk$ is a field of…
We construct a `weak' version EM^w(K) of Lack & Street's 2-category of monads in a 2-category K, by replacing their compatibility constraint of 1-cells with the units of monads by an additional condition on the 2-cells. A relation between…
The diagonal lemma asserts that if a map of bisimplicial sets is a levelwise weak equivalence in the Kan-Quillen model structure, then it induces a weak equivalence of the diagonal simplicial sets. In this short note, we observe that the…
Fix a field $k$. When $\Delta$ is a simplicial complex on $n$ vertices with Stanley-Reisner ideal $I_\Delta$, we define and study an invariant called the $\textit{type defect}$ of $\Delta$. Except when $\Delta$ is of a single simplex, the…
In this paper we redevelop the foundations of the category theory of quasi-categories (also called infinity-categories) using 2-category theory. We show that Joyal's strict 2-category of quasi-categories admits certain weak 2-limits, among…
We examine a condition on a simply connected 2-complex X ensuring that groups acting properly on X are coherent. This extends earlier work on 2-complexes with negative sectional curvature which covers the case that G acts freely. Our…
Both simplicial sets and simplicial spaces are used pervasively in homotopy theory as presentations of spaces, where in both cases we extract the "underlying space" by taking geometric realization. We have a good handle on the category of…
Algebraic geometry, although little explored in signal processing, provides tools that are very convenient for investigating generic properties in a wide range of applications. Generic properties are properties that hold "almost…
The behaviour of limits of weak morphisms in 2-dimensional universal algebra is not 2-categorical in that, to fully express the behaviour that occurs, one needs to be able to quantify over strict morphisms amongst the weaker kinds.…
We prove a rigidity theorem for the Poisson automorphisms of the function fields of tori with quadratic Poisson structures over fields of characteristic 0. It gives an effective method for classifying the full Poisson automorphism groups of…
If a locally cartesian closed category carries a weak factorisation system, then the left maps are stable under pullback along right maps if and only if the right maps are closed under pushforward along right maps. We refer to this…
It is proved that the space of differential forms with weak exterior and co-derivative, is compactly embedded into the space of square integrable differential forms. Mixed boundary conditions on weak Lipschitz domains are considered.…
Eight categorical soundness and completeness theorems are established within the framework of algebraic theories. Exactly six of the eight deduction systems exhibit complete semantics within the cartesian monoidal category of sets. The…
Given an infinite field $\mathbb{k}$ and a simplicial complex $\Delta$, a common theme in studying the $f$- and $h$-vectors of $\Delta$ has been the consideration of the Hilbert series of the Stanley--Reisner ring $\mathbb{k}[\Delta]$…
In this paper, we give a new and efficient algebraic criterion for the pure as well as non-pure shellability of simplicial complex $\Delta$ over [n]. We also give an algebraic characterization of a leaf in a simplicial complex (defined in…
The aim of these notes is to introduce the intuition motivating the notion of a "complicial set", a simplicial set with certain marked "thin" simplices that witness a composition relation between the simplices on their boundary. By varying…
We show that the Golod property of a Stanley-Reisner ring can depend on the characteristic of the base field. More precisely, for every finite set $T$ of prime numbers we construct simplicial complexes $\Delta$ and $\Gamma$, such that…