Two remarks on spaces of maps between operads of little cubes

Geoffroy Horel; Manuel Krannich; Alexander Kupers

doi:10.21136/HS.2025.07

paper

Two remarks on spaces of maps between operads of little cubes

arXiv:2211.00908 · doi:10.21136/HS.2025.07

Abstract

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.

10 pages; published version