Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A categorical construction for the computational definition of vector
  spaces   Lambda-S is an extension to first-order lambda calculus unifying two
approaches of non-cloning in quantum lambda-calculi. One is to forbid
duplication of variables, while the other is to consider all lambda-terms as
algebraic linear functions. The type system of Lambda-S has a constructor S
such that a type A is considered as the base of a vector space while S(A) is
its span. Lambda-S can also be seen as a language for the computational
manipulation of vector spaces: The vector spaces axioms are given as a rewrite
system, describing the computational steps to be performed. In this paper we
give an abstract categorical semantics of Lambda-S* (a fragment of Lambda-S),
showing that S can be interpreted as the composition of two functors in an
adjunction relation between a Cartesian category and an additive symmetric
monoidal category. The right adjoint is a forgetful functor U, which is hidden
in the language, and plays a central role in the computational reasoning.

20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con