Related papers: Graded Tambara Functors

In the previous article 'A Mackey-functor theoretic interpretation of biset functors', we have constructed the 2-category $\mathbb{S}$ of finite sets with variable finite group actions, in which bicoproducts and bipullbacks exist. As shown…

We construct a faithful and conservative functor from prisms to $C_{p^\infty}$-Tambara functors; in appropriate situations, this gives an algebraic description of $\underline\pi_0{\mathrm{TC}^-}$. We also present two integral variants using…

Given commutative, unital rings $A$ and $B$ with a ring homomorphism $A\to B$ making $B$ free of finite rank as an $A$-module, we can ask for a "trace" or "norm" homomorphism taking algebraic data over $B$ to algebraic data over $A$. In…

We show that various flavors of Witt vectors are functorial with respect to multiplicative polynomial laws of finite degree. We then deduce that the $p$-typical Witt vectors are functorial in multiplicative polynomial maps of degree at most…

We construct a functor from the category of admissible finitely presented o-representations of GL(2,F) to the category of finite length o-representations of Gal_{Q_p}, for any finite extension F of Q_p and the ring of integers o of a finite…

This paper aims at setting out the basics of $\mathbb{Z}$-graded manifolds theory. We introduce $\mathbb{Z}$-graded manifolds from local models and give some of their properties. The requirement to work with a completed graded symmetric…

In the first part of this note, we review and compare various instances of the notion of twisted coefficient system, a.k.a. polynomial functor, appearing in the literature. This notion hinges on how one defines the degree of a functor from…

RO*-algebras are defined and studied. For RO*-algebra T, using properties of partial order, it is established that the set of bounded elements can be endowed with C*-norm. The structure of commutative subalgebras of T is considered and the…

We present some properties of the gradient of a mu-differentiable function. The Method of Lagrange Multipliers for mu-differentiable functions is then exemplified.

We here first study the state space realization of a tensor-product of a pair of rational functions. At the expense of "inflating" the dimensions, we recover the classical expressions for realization of a regular product of rational…

It is characterized when coarsening functors between categories of graded modules preserve injectivity of objects, and when they commute with graded covariant Hom functors.

We prove that any derived equivalence between triangular algebras is standard, that is, it is isomorphic to the derived tensor functor given by a two-sided tilting complex.

For a finite group $G$, (semi-)Mackey functors and (semi-)Tambara functors are regarded as $G$-bivariant analogs of (semi-)groups and (semi-)rings respectively. In fact if $G$ is trivial, they agree with the ordinary (semi-)groups and…

In this paper, we extend the notion of modular functor and fusion category to what we called $G$ equivariant modular functor and $G$ equivariant fusion category, where $G$ is a finite group, and establish a correspondence between between…

We define the Hall algebra associated to any triangulated category under some finiteness conditions with the $t$-periodic translation functor $T$ for odd $t>1.$ This generalizes the results in \cite{Toen2005} and \cite{XX2006}.

We give a short proof for a well-known formula for the rank of a $G$-crossed braided extension of a modular tensor category.

It is well known that a non-negative definite polynomial matrix (a polynomial Gramian) $G(t)$ can be written as a product of its polynomial spectral factors, $G(t) = X(t)^H X(t)$. In this paper, we give a new algebraic characterization of…

We define the induction and restriction functors for cyclotomic q-Schur algebras, and study some properties of them. As an application, we categorify a higher level Fock space by using the module categories of cyclotomic q-Schur algebras.

We construct a stratification on the Nakaoka spectrum of any $G$-Tambara functor indexed by the poset of subgroups of $G$. When $G$ is Dedekind, we show that the $H$th stratum of the Nakaoka spectrum of the Burnside $G$-Tambara functor is…

In the first part we deepen the six-functor theory of (holonomic) logarithmic D-modules, in particular with respect to duality and pushforward along projective morphisms. Then, inspired by work of Ogus, we define a logarithmic analogue of…