Two remarks on spaces of maps between operads of little cubes

Alexander Kupers; Geoffroy Horel; Manuel Krannich

arxiv: 2211.00908 · v3 · pith:NAP6ZQULnew · submitted 2022-11-02 · 🧮 math.AT · math.CT

Two remarks on spaces of maps between operads of little cubes

Geoffroy Horel , Manuel Krannich , Alexander Kupers This is my paper

classification 🧮 math.AT math.CT

keywords spacescubeslittlemappingmapsoperadsversionsautomorphisms

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We record two facts on spaces of derived maps between the operads $E_d$ of little $d$-cubes. Firstly, these mapping spaces are equivalent to the mapping spaces between the non-unitary versions of $E_d$. Secondly, all endomorphisms of $E_d$ are automorphisms. We also discuss variants for localisations of $E_d$ and for versions with tangential structures.

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Universal Properties of Variations of the Little Cubes Operads
math.AT 2024-06 unverdicted novelty 6.0

Proves universal property for parametrized little cubes operad E_B showing it as colimit of E_n over B, with descent for factorization algebras.