9 problems

Let $k$ be a field of characteristic zero, let $I$ be the unit for the tensor product, and let $x$ be an object of dimension $n$ with $n$th exterior power $\Lambda^n(x)$. The speci…

Coherent associativity conjecture. The bifunctor $\otimes^K_0$ is coherently associative. This would strengthen the displayed associativity isomorphism to coherent associativity of…

Injectivity and order-preserving image conjecture. This homomorphism is injective, and its image consists precisely of the order-preserving automorphisms.

Gainutdinov–Runkel's conjecture. The pseudo-$q$-trace construction yields a linear isomorphism

Let $k$ be an algebraically closed field of characteristic zero, let $I$ be the unit for the tensor product, and let $x$ be an object of dimension $n$ equipped with an isomorphism…

Let $k$ be an algebraically closed field of characteristic zero, let $I$ be the unit for the tensor product, and let $x$ be a self-dual object of dimension $n$. Let…

Let $k$ be a field of characteristic zero, let $I$ be the unit for the tensor product, and let $x$ be a self-dual object of dimension $n$. Let $\epsilon\colon x\otimes x\to I$ be i…

Let $k$ be a field of characteristic zero. A 2-rig is the representation-theoretic structure in which the stated universal property is considered; let $x$ be an object, let $n$ be…

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…