We study the circumstances under which one can reconstruct a stack from its associated functor of isomorphism classes. This is possible surprisingly often: we show that many of the standard examples of moduli stacks are determined by their functors. Our methods seem to exhibit new anabelian-type phenomena, in the form of structures in the category of schemes that encode automorphism data in gro...

We show, for an arbitrary adjunction F U : B → A with B Cauchy complete, that the functor F is comonadic if and only if the monad T on A induced by the adjunction is of effective descent type, meaning that the free T-algebra functor F : A → AT is comonadic. This result is applied to several situations: In Section 4 to give a sufficient condition for an exponential functor on a cartesian closed ...

Let R be a (unital) commutative ring, andG be a finite group with order invertible in R. We introduce new idempotents εT,S in the double Burnside algebra RB(G,G) of G over R, indexed by conjugacy classes of minimal sections (T, S) of G (i.e. sections such that S ≤ Φ(T )). These idempotents are orthogonal, and their sum is equal to the identity. It follows that for any biset functor F over R, th...

A squarefree module over a polynomial ring S = k[x1, . . . , xn] is a generalization of a Stanley-Reisner ring, and allows us to apply homological methods to the study of monomial ideals more systematically. The category Sq of squarefree modules is equivalent to the category of finitely generated left Λ-modules, where Λ is the incidence algebra of the Boolean lattice 2. The derived category D(S...

We introduce and discuss the notion of naturally full func-tor. The definition is similar to the definition of separable functor: a naturally full functor is a functorial version of a full functor, while a separable functor is a functorial version of a faithful functor. We study general properties of naturally full functors. We also discuss when func-tors between module categories and between c...

The classical Poisson functor associates to every infinite measure preserving dynamical system (X, μ, T) a probability (X*, μ*, T*) called the suspension of T. In this paper we generalize construction: subgroup Aut2(X, μ) μ-nonsingular transformations T X is specified as largest for which T* μ*-nonsingular. topological structure studied. We show that generic element in ergodic and Krieger type ...

in this paper we show that expansion of a buchsbaum simplicial complex is $cm_t$, for an optimal integer $tgeq 1$. also, by imposing extra assumptions on a $cm_t$ simplicial complex, we provethat it can be obtained from a buchsbaum complex.

The articles [16], [19], [20], [2], [21], [4], [9], [3], [1], [11], [15], [5], [17], [18], [10], [7], [8], [6], [13], [22], [12], and [14] provide the notation and terminology for this paper. We use the following convention: n is a natural number, x, X, X1 are sets, and s, r, p are real numbers. Let S, T be 1-sorted structures. A partial function from S to T is a partial function from the carri...

Let $R$ be a commutative ring. We write $mbox{Hom}(mu_A, nu_B)$ for the set of all fuzzy $R$-morphisms from $mu_A$ to $nu_B$, where $mu_A$ and $nu_B$ are two fuzzy $R$-modules. We make$mbox{Hom}(mu_A, nu_B)$ into fuzzy $R$-module by redefining a function $alpha:mbox{Hom}(mu_A, nu_B)longrightarrow [0,1]$. We study the properties of the functor $mbox{Hom}(mu_A,-):FRmbox{-Mod}rightarrow FRmbox{-Mo...