Resolves Arkor's conjecture with equivalent characterizations of exponentiable virtual double categories via cell decompositions and proves several classes including cospans are exponentiable.
δ[n−1,n] ∗ ) : Q[n] → Q[1] ×Q[0] · · · ×Q[0] Q[1] in Cat = Prof0 induced by the functors from (1), for the inert morphisms δ[i,i+1] : [1] → [n], is an isomorphism
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2026 1verdicts
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Exponentiable Virtual Double Categories and Representability of Exponentials
Resolves Arkor's conjecture with equivalent characterizations of exponentiable virtual double categories via cell decompositions and proves several classes including cospans are exponentiable.