Fall 2017 Goodwillie Calculus Seminar
نویسندگان
چکیده
We want F to satisfy some kind of Mayer-Vietoris property, or excision. Hence, we assume C and D are proper, in that the pushout of a weak equivalence along a cofibration is also a weak equivalence. We’ll also ask that in D, sequential colimits of homotopy Cartesian cubes are again homotopy Cartesian, and we’ll elaborate on what this means. We also place a condition on F : Goodwillie calls it “continuous,” meaning that it’s an enriched functor: the induced map MapC(X,Y ) −→ MapD(F (X), F (Y )) is a continuous map between topological spaces (or a morphism of simplicial sets; for the rest of this section, we’ll let V denote the choice of Top∗ or sSet∗ that we made). If X ∈ C and K ∈ V, then we have a tensor-hom adjunction C(X ⊗K,Y ) ∼= V(K,C(X,Y )).
منابع مشابه
An Introduction to Goodwillie Calculus
We introduce the main definitions and structural theorems from Goodwillie Calculus. Most of the material in these notes is taken from [3, §§6.1.1–6.1.4]. These notes are rough — use at own risk! Corrections welcome.
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