Übersetzung für 'topos' von Englisch nach Deutsch

topos

Topos {m}lit.philos.rhet.

• 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".

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• 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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