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- W2890403024 abstract "We prove that every elementary $(infty,1)$-topos has a natural number object. We achieve this by defining the loop space of the circle and showing that we can construct a natural number object out of it. Part of the proof involves showing that various definitions of natural number objects (Lawvere, Freyd and Peano) agree with each other in an elementary $(infty,1)$-topos. As part of this effort we also study the internal object of contractibility in $(infty,1)$-categories, which is of independent interest. Finally, we discuss various applications of natural number objects. In particular, we use it to define internal sequential colimits in an elementary $(infty,1)$-topos." @default.
- W2890403024 created "2018-09-27" @default.
- W2890403024 creator A5022311151 @default.
- W2890403024 date "2018-09-05" @default.
- W2890403024 modified "2023-09-27" @default.
- W2890403024 title "Every Elementary Higher Topos has a Natural Number Object." @default.
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