ScalingStacks

[0MHM]

Corollary 3.7. Suppose 0≤k≤n0\leq k\leq n. Then the smallest full subcategory of Gauntn\gaunt_{n} that is closed under colimits and contains the cells CrC_{r} for r≤kr\leq k is Gauntk\gaunt_{k}.

[0MHN]

Proof. The inclusion of gaunt kk-categories commutes with colimits (as it admits a right adjoint, see Rk. 3.2), whence it is enough to consider the case k=nk=n. This now follows readily from Corollary 3.4 and Proposition 2.7. ∎

Original mathematics by the credited authors. Source collection and HTML conversion remain in progress.

Clark Barwick, Christopher Schommer-Pries

Original source: arXiv:1112.0040v6

Original source · 1112.0040v6