We study stabilization of finite-dimensional representations the periplectic Lie superalgebras $\mathfrak{p}(n)$ as $n \to \infty$. The paper gives a construction tensor category $Rep(\underline{P})$, possessing nice universal properties among categories over $\mathtt{sVect}$ complex vector superspaces. First, it is abelian envelope Deligne corresponding to superalgebra, in sense arXiv:1511...

We construct a category of fibrant objects C〈P〉 in the sense K. Brown from any indexed frame (a kind poset generalizing triposes) P, and show that its homotopy is Barr-exact C[P] partial equivalence relations compatible functional relations. In particular this gives presentation realizability toposes as categories. give criteria for existence left right derived functors to C〈Φ〉:C〈P〉→C〈Q〉 induce...

Abstract For ℳ and $$ \mathcal{N} N finite module categories over a tensor category \mathcal{C} C , the \mathrm{\mathcal{R}}{ex}_{\mathcal{C}} ℛ ex (ℳ, ) of right exact functors is Drinfeld center \mathcal{Z} Z ( ). We ...

In this paper we present an example of elaborate categorical structures hidden in very simple algebraic objects. We look at the algebra of polynomial differential operators in one variable x, also known as the Weyl algebra, and its irreducible representation in the ring of polynomials Q[x]. We construct an abelian category C whose Grothendieck group can be naturally identified with the ring of ...

This paper establishes two new connections between the familiar function ring functor ${mathfrak R}$ on the category ${bf CRFrm}$ of completely regular frames and the category {bf CR}${mathbf sigma}${bf Frm} of completely regular $sigma$-frames as well as their counterparts for the analogous functor ${mathfrak Z}$ on the category {bf ODFrm} of 0-dimensional frames, given by the integer-valued f...

We establish axiomatic characterizations of K-theory and KK-theory for real C*-algebras. In particular, let F be an abelian group-valued functor on separable real C*-algebras. We prove that if F is homotopy invariant, stable, and split exact, then F factors through the category KK. Also, if F is homotopy invariant, stable, half exact, continuous, and satisfies an appropriate dimension axiom, th...

Bivariant (equivariant) K-theory is the standard setting for noncommutative topology. We may carry over various techniques from homotopy theory and homological algebra to this setting. Here we do this for some basic notions from homological algebra: phantom maps, exact chain complexes, projective resolutions, and derived functors. We introduce these notions and apply them to examples from bivar...