IntroductionThe stable motivic homotopy categories of schemes are nice ∞-categories, which admit a whole six-functor formalism. For a smooth morphism of schemes f: X→Y over a base S, the usual pullback functor f*: SH(Y)→SH(X) admits a left adjoint f_♯, the additive pushforward; they are packaged in a functor from an ∞-category of spans.Recently, Bachmann and Hoyois discovered a multiplicat...
PrerequisiteSome basic knowledge of quantum mechanics and category theory. Background in logic or algebraic/differential geometry would be helpful.AbstractA topos is a mathematical structure which resembles the category of sets, and furthermore has a notion of localization. This structure has an internal logic associated to it, in which true-false logic may be replaced by multi-valued logic. To...
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