ScalingStacks

Definition 2.3. The category ${\mathbb{R}}^{3}\boldsymbol{\mathrm{Link}}^{\circ}$ has objects given by embedded, framed oriented links in $L\subset{\mathbb{R}}^{3}$, such that the projection along the $z$-axis maps $L$ to a blackboard-framed link diagram in ${\mathbb{R}}^{2}\times\{0\}\subset{\mathbb{R}}^{3}$, together with an ordering of the finitely many crossings in the diagram. The morphisms are oriented link cobordisms in ${\mathbb{R}}^{3}\times{[0,1]}$ up to isotopy rel boundary, together with formal crossing reordering isomorphisms.