A bstract We investigate the fusion of B-type interfaces in two-dimensional supersymmetric Landau-Ginzburg models. In particular, we propose to describe an interface terms a functor that acts on category modules underlying polynomial rings chiral superfields. This uplift matrix factorisations simplifies actual computation fusion. Besides brief discussion minimal models, illustrate power this ap...

Functors preserving weak pullbacks provide the basis for a rich structure theory of coalgebras. We give an easy to use criterion to check whether a functor preserves weak pullbacks. We apply the characterization to the functor F which associates a set X with the set F(X) of all filters on X. It turns out that this functor preserves weak pullbacks, yet does not preserve weak generalized pullback...

We consider the question of defining interleaving metrics on generalized persistence modules over arbitrary preordered sets. Our constructions are functorial, which implies a form of stability for these metrics. We describe a large class of examples, inverseimage persistence modules, which occur whenever a topological space is mapped to a metric space. Several standard theories of persistence a...

The well known isomorphism relating the rational algebraic K-theory groups and the rational motivic cohomology groups of a smooth variety over a field of characteristic 0 is shown to be realized by a map (the “Segre map”) of infinite loop spaces. Moreover, the associated Chern character map on rational homotopy groups is shown to be a ring isomorphism. A technique is introduced which establishe...

We show that the homotopy category of simplicial diagrams I-SS indexed by a small category I is equivalent to a homotopy category of SS ↓ NI simplicial sets over the nerve NI. Then their equivalences, by means of the nerve functor N : Cat → SS from the category Cat of small categories, with respective homotopy categories associated to Cat are established. Consequently, an equivariant simplicial...

Motivation and background. Motivated by ideas from string theory and quantum field theory new invariants of knots and 3-dimensional manifolds have been constructed from complex algebraic structures such as Hopf algebras [17] [22], monoidal categories with additional structure [24], and modular functors [14] [23]. These constructions are closely related. Here we take a unifying categorical appro...

Let G be a finite group. For a based G-space X and a Mackey functor M , a topological Mackey functor X e ⊗M is constructed. When X is a based G-CW complex, X e ⊗M is shown to be an infinite loop space in the sense of G-spaces. This gives a version of the RO(G)-graded equivariant Dold-Thom theorem. Applying a variant of Elmendorf’s construction, we get a model for the Eilenberg-Mac Lane spectrum...

Let Var be the category of complex algebraic varieties, Top that of nice topological spaces, Dab be the derived category of finite complexes of finitely generated abelian groups. One has tensor functors Var → Top → Dab, the first assigns to a variety its space equipped with the classical topology, the second one is the singular chain complex functor (the tensor structure for the first two categ...

Abstract We equate various Euler classes of algebraic vector bundles, including those [12] and one suggested by M. J. Hopkins, A. Raksit, J.-P. Serre. establish integrality results for this class give formulas local indices at isolated zeros, both in terms the six-functors formalism coherent sheaves as an explicit recipe commutative algebra Scheja Storch. As application, we compute enriched bil...

We prove that for a topological operad P the operad of oriented cubical chains, C ∗ (P ), and the operad of singular chains, S∗(P ), are weakly equivalent. As a consequence, C ord ∗ (P ;Q) is formal if and only if S∗(P ;Q) is formal, thus linking together some formality results that are spread out in the literature. The proof is based on an acyclic models theorem for monoidal functors. We give ...