nLab
arrow (∞,1)-topos

Contents

Definition

For H\mathbf{H} an (∞,1)-topos, its arrow (,1)(\infty,1)-topos is its arrow (∞,1)-category.

Properties

For (X defι XX bulk)(X_{def} \stackrel{\iota_X}{\to} X_{bulk}) and (A defFA bulk)(A_{def} \stackrel{\mathbf{F}}{\to} A_{bulk}) in H Δ 1\mathbf{H}^{\Delta^1}, there is an (∞,1)-pullback diagram

H Δ 1(ι X,F) H(X def,A def) H(X bulk,A bulk) H(X def,A bulk). \array{ \mathbf{H}^{\Delta^1}(\iota_X, \mathbf{F}) &\stackrel{}{\to}& \mathbf{H}(X_{def}, A_{def}) \\ \downarrow &\swArrow& \downarrow \\ \mathbf{H}(X_{bulk}, A_{bulk}) &\to& \mathbf{H}(X_{def}, A_{bulk}) } \,.

Note: ‘def’ and ‘bulk’ indicate terms of fields in a QFT with defects.

Last revised on July 6, 2016 at 06:43:36. See the history of this page for a list of all contributions to it.