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research article

Every Elementary Higher Topos Has A Natural Number Object

Rasekh, Nima  
January 1, 2021
Theory And Applications Of Categories

We prove that every elementary (infinity, 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 (infinity, 1)-topos. As part of this effort we also study the internal object of contractibility in (infinity, 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 (infinity, 1)-topos.

  • Details
  • Metrics
Type
research article
Web of Science ID

WOS:000674967700013

Author(s)
Rasekh, Nima  
Date Issued

2021-01-01

Published in
Theory And Applications Of Categories
Volume

37

Start page

337

End page

377

Subjects

Mathematics, Applied

•

Mathematics

•

Mathematics

•

elementary topos theory

•

higher category theory

•

natural number objects

URL

Link to the fulltext

http://www.tac.mta.ca/tac/volumes/37/13/37-13.pdf
Editorial or Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
UPHESS  
Available on Infoscience
July 31, 2021
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/180246
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