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Derived Algebraic Geometry II: Noncommutative Algebra
[article]

Jacob Lurie

2007
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arXiv
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pre-print

(*ii*) For every vertex k of K, the image of {k} ⊲ *under* f is a p-coCartesian morphism of X. (iii) There exists a vertex k of K such that the image of {k} ⊲ *under* f is a p-coCartesian morphism of X. ...
More *informally*, a functor f : N(J 0 ) → C ⊗ belongs to E 0 (C) if there exists an object C = f ( 1 * ) ∈ C, such that for all n ≥ 0, the object f ( n * ) ∈ C ⊗ n * corresponds to (C, C, . . . , C) *under* ...
Assertion (i) follows immediately from the stability of C *under* finite coproducts. We now prove (*ii*). Suppose given a pair of maps f : X → N and g : Y → N , respectively. ...

arXiv:math/0702299v5
fatcat:6tdcjvtqtjctvlqxahu7kvrtcu