Related papers: FI-calculus and representation stability

For a nice-enough category $\mathcal{C}$, we construct both the morphism category ${\rm H}(\mathcal{C})$ of $\mathcal{C}$ and the category ${\rm mod}\mbox{-}\mathcal{C}$ of all finitely presented contravariant additive functors over…

We define triangulated factorization systems on triangulated categories, and prove that a suitable subclass thereof (the normal triangulated torsion theories) corresponds bijectively to $t$-structures on the same category. This result is…

For a countable group $G$ we construct a small, idempotent complete, symmetric monoidal, stable $\infty$-category $\mathrm{KK}^{G}_{\mathrm{sep}}$ whose homotopy category recovers the triangulated equivariant Kasparov category of separable…

We consider in parallel pointed homotopy automorphisms of iterated wedge sums of topological spaces and boundary relative homotopy automorphisms of iterated connected sums of manifolds minus a disk. Under certain conditions on the spaces…

We consider a subclass of the class of group-theoretical fusion categories: To every finite group $G$ and subgroup $H$ one can associate the category of $G$-graded vector spaces with a two-sided $H$-action compatible with the grading. We…

In this paper we consider the locally self-injective property of the product FI$^m$ of the category FI of finite sets and injections. Explicitly, we prove that the external tensor product commutes with the coinduction functor, and hence…

The $k$-dimensional functional order property ($\text{FOP}_k$) is a combinatorial property of a $(k+1)$-partitioned formula. This notion arose in work of Terry and Wolf, which identified $\text{NFOP}_2$ as a ternary analogue of stability in…

In this paper we develop machinery for studying sequences of representations of any of the three families of classical Weyl groups, extending work of Church, Ellenberg, Farb, and Nagpal on the symmetric groups S_n to the signed permutation…

We use a recently proposed formulation of stable holomorphic vector bundles $V$ on elliptically fibered Calabi--Yau n-fold $Z_n$ in terms of toric geometry to describe stability conditions on $V$. Using the toric map $f: W_{n+1} \to…

A stable $\infty$-category is $1$-semiadditive if the norms for all finite group actions are equivalences. In the presence of $1$-semiadditivity, Goodwillie calculus simplifies drastically. We introduce two variants of $1$-semiadditivity…

We prove a structure theorem for stable functions on amenable groups, which extends the arithmetic regularity lemma for stable subsets of finite groups. Given a group $G$, a function $f\colon G\to [-1,1]$ is called stable if the binary…

We construct a calculus of functors in the spirit of orthogonal calculus, which is designed to study "functors with reality" such as the Real classifying space functor, $BU_\mathbb{R}(-)$. The calculus produces a Taylor tower, the $n$-th…

In this paper, we investigate the properties of the category of equivariant diagram spectra indexed on the category W_G of based G-spaces homeomorphic to finite G-CW-complexes for a compact Lie group G. Using the machinery of Mandell, May,…

We investigate correspondence functors, namely the functors from the category of finite sets and correspondences to the category of $k$-modules, where $k$ is a commutative ring.They have various specific properties which do not hold for…

In this paper, we analyze the smoothness and stability of hidden variable recurrent fractal interpolation functions (HVRFIF) with function contractivity factors introduced in Ref. 1. The HVRFIF is a hidden variable fractal interpolation…

Goodwillie's homotopy functor calculus constructs a Taylor tower of approximations to F, often a functor from spaces to spaces. Weiss's orthogonal calculus provides a Taylor tower for functors from vector spaces to spaces. In particular,…

We construct a Wach module for the absolutely semi-stable representations the filtered $(\varphi, N)$-module of which satisfies the Griffiths transversality, which happens in particular for ordinary representations. This construction…

We describe a new approach to the definition of the moduli functor of stable varieties. While there is wide agreement as to what classes of varieties should appear, the notion of a family of stable surfaces is quite subtle, as key numerical…

We classify all irreducible generic $\mathrm{VI}$-modules in non-describing characteristic. Our result degenerates to yield a classification of irreducible generic $\mathrm{FI}$-modules in arbitrary characteristic. Our result can also be…

We study the end-behavior of integer-valued FI-modules. Our first result describes the high degrees of an FI-module in terms of newly defined tail invariants. Our main result provides an equivalence of categories between FI-tails and…