Crossed modules as homotopy normal maps |
| |
Authors: | Emmanuel D Farjoun Yoav Segev |
| |
Institution: | a Department of Mathematics, Hebrew University of Jerusalem, Givat Ram, Jerusalem 91904, Israel b Department of Mathematics, Ben Gurion University, Beer Sheva, Israel |
| |
Abstract: | In this note we consider crossed modules of groups (N→G, G→Aut(N)), as a homotopy version of the inclusion N⊂G of a normal subgroup. Our main observation is a characterization of the underlying map N→G of a crossed module in terms of a simplicial group structure on the associated bar construction. This approach allows for “natural” generalizations to other monoidal categories, in particular we consider briefly what we call “normal maps” between simplicial groups. |
| |
Keywords: | primary 20J05 18G30 secondary 55U10 |
本文献已被 ScienceDirect 等数据库收录! |
|