On Costello’s Construction of the Witten Genus: Mapping Spaces
نویسنده
چکیده
1. DERIVED GEOMETRY WITH L∞ ALGEBRAS We are interested in studying formal derived moduli problems, as an orienting remark recall that particularly nice simplicial sets are those that are Kan complexes and that the nerve of a category C is Kan complex if and only if C is a groupoid. Consider the following progression. • Schemes: Functors from commutative algebras to sets; • Stacks: Functors from commutative algebras to groupoids; • Higher Stacks: Functors from commutative algebras to simplicial sets; • Derived Stacks: Functors from dg commutative algebras to simplicial sets Further, the adjective formal restricts the domain category to (local) Artinian algebras.1 We make the following definition.
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