# reference request – Product Smash and integers in a Grothendieck \$ ( infty, 1) \$ – topos

Let $$mathcal {H}$$ to be a Grothendieck $$( infty, 1)$$-topos. According to this page in nlab, for all $$X in mathcal {H}$$, the object suspension $$Sigma X$$ is homotopy equivalent to the smash product $$B mathbb {Z} wedge X$$, or $$B mathbb {Z}$$ is "the discrete group's classification space of integers". In addition, for any sharp object $$X in mathcal {H} _ *$$ and any group object $$G in Grp ( mathcal {H})$$, the article says we can "train the tensor product $$X otimes G in Grp ( mathcal {H})$$. "

My problem is this: none of these terminologies are explained, and the page does not provide any reference. More specifically, what is $$mathbb {Z}$$ in an arbitrary $$infty$$-topos? What is the smash product $$wedge$$? What is the tensor product $$otimes$$? My best guess is that $$otimes$$ refers to the unique tensor structure on $$mathcal {H} _ *$$ such as the map $$mathcal {H} to mathcal {H} _ *$$ is monoidal symmetric (here $$mathcal {H}$$ is given the Cartesian monoidal structure), but this is only a conjecture.

Is there a reference where all these notions are defined?