Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Types and forgetfulness in categorical linguistics and quantum mechanics   The role of types in categorical models of meaning is investigated. A general
scheme for how typed models of meaning may be used to compare sentences,
regardless of their grammatical structure is described, and a toy example is
used as an illustration. Taking as a starting point the question of whether the
evaluation of such a type system 'loses information', we consider the
parametrized typing associated with connectives from this viewpoint.
  The answer to this question implies that, within full categorical models of
meaning, the objects associated with types must exhibit a simple but subtle
categorical property known as self-similarity. We investigate the category
theory behind this, with explicit reference to typed systems, and their
monoidal closed structure. We then demonstrate close connections between such
self-similar structures and dagger Frobenius algebras. In particular, we
demonstrate that the categorical structures implied by the polymorphically
typed connectives give rise to a (lax unitless) form of the special forms of
Frobenius algebras known as classical structures, used heavily in abstract
categorical approaches to quantum mechanics.

10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex