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arXiv · 2605.30835

The group of homotopy self-equivalences is a Lax functor

Toshihiro Yamaguchi·Shoji Yokura
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Abstract

The group $\E(X)$ of homotopy self-equivalences of a topological space $X$ is a well-known group in homotopy theory and has been studied by many people since it was first introduced in the late 1950s. $\E$ is not a functor in the usual sense. In this paper we show that $\E$ is a Lax functor from the category $\mathscr Top$ of topological spaces to a strict $2$-category $\op{Corr}_{\mathscr Gr}$ of \emph{correspondences} of groups.

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Toshihiro Yamaguchi, Shoji Yokura. 2026-05-29. The group of homotopy self-equivalences is a Lax functor. https://arxiv.org/abs/2605.30835

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