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 ⇄Suchrichtung
 Übersetzung für 'topos' von Englisch nach Deutsch
NOUN1   a topo | topos
NOUN2   topos | topoi / toposes
lit.philos.rhet.
topos
Topos {m}
8
1 Übersetzung
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 ⇄ 
Übersetzung für 'topos' von Englisch nach Deutsch

topos
Topos {m}lit.philos.rhet.
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Anwendungsbeispiele Englisch
  • Lawvere and Tierney therefore formulated axioms for a topos that assumed a sub-object classifier, and some limit conditions (to make a cartesian-closed category, at least).
  • A category of sheaves on a site is called a "topos" or a "Grothendieck topos".
  • He invented or developed a broad range of fundamental ideas in topos theory.
  • corresponds to any subobject having a complement, in which case we call the topos Boolean.
  • Precisely, in Lurie's "Higher Topos Theory", an ∞-topos is defined as an ∞-category "X" such that there is a small ∞-category "C" and a left exact localization functor from the ∞-category of presheaves of spaces on "C" to "X".

  • If one replaces a "topos" by an ∞-topos, then one gets the notion of a ringed ∞-topos.
  • Both examples above are subsumed by the following general fact: every elementary topos, defined as a category with finite limits and power objects, necessarily has a subobject classifier.
  • Every Grothendieck topos is an elementary topos, but the converse is not true (since every Grothendieck topos is cocomplete, which is not required from an elementary topos).
  • With this notion of morphism, the collection of all "G"-sets forms a category; this category is a Grothendieck topos (in fact, assuming a classical metalogic, this topos will even be Boolean).
  • Fix a topos [...] and let all algebras be algebras over it.

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