Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Congruences of fork extensions of slim semimodular lattices   For a slim, planar, semimodular lattice $L$ and covering square~$S$,
G.~Cz\'edli and E.\,T.~Schmidt introduced the fork extension, $L[S]$, which is
also a slim, planar, semimodular lattice. We investigate when a congruence of
$L$ extends to $L[S]$.
  We introduce a join-irreducible congruence $\boldsymbol{\gamma}(S)$ of
$L[S]$. We determine when it is new, in the sense that it is not generated by a
join-irreducible congruence of $L$. When it is new, we describe the congruence
$\boldsymbol{\gamma}(S)$ in great detail. The main result follows: \emph{In the
order of join-irreducible congruences of a slim, planar, semimodular lattice
$L$, the congruence $\boldsymbol{\gamma}(S)$ has \emph{at most two covers.}}

22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin