nLab
n-reduced (∞,1)-functor

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Definition

In the context of Goodwillie calculus, an (∞,1)-functor is called nn-reduced for nn \in \mathbb{N}, n>0n \gt 0, if its (n-1)-excisive approximation is trivial, P n1F*P_{n-1} F \simeq \ast (hence if it is a P n1P_{n-1} anti-modal type).

(e.g. Lurie, def. 6.1.2.1)

Hence a functor is 1-reduced (or just reduced, for short), if F(*)*F(\ast) \simeq \ast.

A functor that is both n-excisive and nn-reduced is called an n-homogeneous (∞,1)-functor.

References

Created on January 6, 2016 at 09:46:48. See the history of this page for a list of all contributions to it.