Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Relative symmetric monoidal closed categories I: Autoenrichment and
  change of base   Symmetric monoidal closed categories may be related to one another not only
by the functors between them but also by enrichment of one in another, and it
was known to G. M. Kelly in the 1960s that there is a very close connection
between these phenomena. In this first part of a two-part series on this
subject, we show that the assignment to each symmetric monoidal closed category
$V$ its associated $V$-enriched category $\underline{V}$ extends to a 2-functor
valued in an op-2-fibred 2-category of symmetric monoidal closed categories
enriched over various bases. For a fixed $V$, we show that this induces a
2-functorial passage from symmetric monoidal closed categories $\textit{over}$
$V$ (i.e., equipped with a morphism to $V$) to symmetric monoidal closed
$V$-categories over $\underline{V}$. As a consequence, we find that the
enriched adjunction determined a symmetric monoidal closed adjunction can be
obtained by applying a 2-functor and, consequently, is an adjunction in the
2-category of symmetric monoidal closed $V$-categories.

22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
16
The categories of this paper are: stat
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ