Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Actads   In this paper, I introduce a new generalization of the concept of an operad,
further generalizing the concept of an opetope introduced by Baez and Dolan,
who used this for the definition of their version of non-strict $n$-categories.
Opetopes arise from iterating a certain construction on operads called the
$+$-construction, starting with monoids. The first step gives rise to plain
operads, i.e. operads without symmetries. The permutation axiom in a symmetric
operad, however, is an additional structure resulting from permutation of
variables, independent of the structure of a monoid. Even though we can apply
the $+$-construction to symmetric operads, there is the possibility of
introducing a completely different kind of permutations on the higher levels by
again permuting variables without regard to the structure on the previous
levels. Defining and investigating these structures is the main purpose of this
paper. The structures obtained in this way is what I call $n$-actads. In
$n$-actads with $n>1$, the permutations on the different levels give rise to a
certain special kind of $n$-fold category. I also explore the concept of
iterated algebras over an $n$-actad (generalizing an algebra and module over an
operad), and various types of iterated units. I give some examples of algebras
over $2$-actads, and show how they can be used to construct certain new
interesting homotopy types of operads. I also discuss a connection between
actads and ordinal notation.

23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom