ScalingStacks

[05WV]

Proof. Consider the commutative square

𝒞X/\textstyle{\mathcal{C}_{X/}\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces}𝒟F(X)/\textstyle{\mathcal{D}_{F\left(X\right)/}\ignorespaces\ignorespaces\ignorespaces\ignorespaces}𝒞\textstyle{\mathcal{C}\ignorespaces\ignorespaces\ignorespaces\ignorespaces}𝒟.\textstyle{\mathcal{D}.}

The vertical functors and the bottom horizontal functor preserve pullbacks. The right vertical functor is conservative. It follows that the top horizontal functor preserves pullbacks as well. ∎

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

Tomer Schlank, Lior Yanovski

Original source: arXiv:1808.06006v3

    Original source page 9

    Original source · 1808.06006v3