Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-associative algebras   A non-associative algebra over a field $\mathbb{K}$ is a $\mathbb{K}$-vector
space $A$ equipped with a bilinear operation \[ {A\times A\to A\colon\;
(x,y)\mapsto x\cdot y=xy}. \] The collection of all non-associative algebras
over $\mathbb{K}$, together with the product-preserving linear maps between
them, forms a variety of algebras: the category $\mathsf{Alg}_\mathbb{K}$. The
multiplication need not satisfy any additional properties, such as
associativity or the existence of a unit. Familiar categories such as the
varieties of associative algebras, Lie algebras, etc. may be found as
subvarieties of $\mathsf{Alg}_\mathbb{K}$ by imposing equations, here
$x(yz)=(xy)z$ (associativity) or $xy =- yx$ and $x(yz)+z(xy)+ y(zx)=0$
(anti-commutativity and the Jacobi identity), respectively.
  The aim of these lectures is to explain some basic notions of categorical
algebra from the point of view of non-associative algebras, and vice versa. As
a rule, the presence of the vector space structure makes things easier to
understand here than in other, less richly structured categories.
  We explore concepts like normal subobjects and quotients, coproducts and
protomodularity. On the other hand, we discuss the role of (non-associative)
polynomials, homogeneous equations, and how additional equations lead to
reflective subcategories.

24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics