The group of homotopy self-equivalences is a Lax functor
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917547236917248 |
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| author | Yamaguchi, Toshihiro Yokura, Shoji |
| author_facet | Yamaguchi, Toshihiro Yokura, Shoji |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_30835 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The group of homotopy self-equivalences is a Lax functor Yamaguchi, Toshihiro Yokura, Shoji Algebraic Topology Category Theory 55P10, 18N10, 18D60, 55Q05 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. |
| title | The group of homotopy self-equivalences is a Lax functor |
| topic | Algebraic Topology Category Theory 55P10, 18N10, 18D60, 55Q05 |
| url | https://arxiv.org/abs/2605.30835 |