We describe a C-linear additive *-autonomous category of Banach spaces. Please note that a correction has been appended to the original version 1 which is maintained here for reference. Also, a proposed example of a *-autonomous category of topological C-linear spaces has been added to version 2.

Abstract. We construct a symmetric monoidal closed category of polynomial endofunctors (as objects) and simulation cells (as morphisms). This structure is defined using universal properties without reference to representing polynomial diagrams and is reminiscent of Day’s convolution on presheaves. We then make this category into a model for intuitionistic linear logic by defining an additive an...

We describe a C-linear additive *-autonomous category of Banach spaces. Please note that a correction has been appended to the original; which is maintained for reference.

We propose new families of models and algorithms for high-dimensional nonparametric learning with joint sparsity constraints. Our approach is based on a regularization method that enforces common sparsity patterns across different function components in a nonparametric additive model. The algorithms employ a coordinate descent approach that is based on a functional soft-thresholding operator. T...

In this paper we propose an approach to homotopical algebra where the basic ingredient is a category with two classes of distinguished morphisms: strong and weak equivalences. These data determine the cofibrant objects by an extension property analogous to the classical lifting property of projective modules. We define a Cartan-Eilenberg category as a category with strong and weak equivalences ...

This is an account of three 1-hour lectures given at the Instructional Conference on Representation Theory of Algebraic Groups and Related Finite Groups, Isaac Newton Institute, Cambridge, 6–11 January 1997. In section 1, we define abelian categories following Grothendieck [12]. We then characterize module categories among abelian categories. Finally we sketch a proof of Mitchell’s full embeddi...

noindent We have two goals in this paper. First, we investigate and construct cofree coalgebras over $n$-representations of quivers, limits and colimits of $n$-representations of quivers, and limits and colimits of coalgebras in the monoidal categories of $n$-representations of quivers. Second, for any given quivers $mathit{Q}_1$,$mathit{Q}_2$,..., $mathit{Q}_n$, we construct a new quiver $math...

We prove the following theorems: 1. If X has strong measure zero and if Y has strong first category, then their algebraic sum has property s0. 2. If X has Hurewicz’s covering property, then it has strong measure zero if, and only if, its algebraic sum with any first category set is a first category set. 3. If X has strong measure zero and Hurewicz’s covering property then its algebraic sum with...

We define a faithful linear monoidal functor from the partition category, and hence Deligne’s category $\mathrm{\underline{Re}p}(S\_t)$, to additive Karoubi envelope of Heisenberg category. show that induced map on Grothendieck rings is injective corresponds Kronecker coproduct symmetric functions.

We construct a geometry of interaction (GoI; dynamic modeling of Gentzen-style cut elimination) for multiplicativeadditive linear logic (MALL) by employing the Bucciarelli–Ehrhard MALL(I) of indexed linear logic to handle the additives. Our construction is an extension to the additives of the Haghverdi–Scott categorical formulation (a multiplicative GoI situation in a traced monoidal category) ...