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New variations on the notion of topos

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New variations on the notion of topos
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19
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28
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CC Attribution 3.0 Unported:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
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Abstract
The notion topos is a prominent member of a family of notions which includes that of abelian category, of locally presentable category and of higher topos. We propose two new members: the notion of locus and that of para-topos. The category of pointed spaces and the category of spectra are examples of loci. The category of small (weak) $n$-categories is an example para-topos for every $n\geq 1$.