3 problems

Let $[?]$ be a 2-rig and let $r\triangleright [?]$ be an object of finite bosonic subdimension. Splitting principle conjecture. There exists a 2-rig $[?]$ and a map of 2-rigs…

Let $k$ be a field and $N$ a positive integer. Let $[?]$ denote the 2-rig of representations of the matrix monoid $[?]$. Free 2-rig conjecture. The 2-rig $[?]$ is the free 2-rig on…

Let $x$ be an object in a 2-rig. Its bosonic dimension is $n$ when $[?]$; its fermionic dimension is $n$ when $[?]$. Dimension versus subdimension conjecture. If $x$ has bosonic di…