Higher dimensional algebras as ideal maps

Year 2020, Volume: 49 Issue: 6, 1865 - 1884, 08.12.2020

Alper Odabas , Erdal Ulualan

https://doi.org/10.15672/hujms.575080

https://izlik.org/JA22CT44WW

Abstract

In this work, we explain the close relationship between an ideal map structure $S\rightarrow End_{R}(R)$ on a homomorphism of commutative $k$-algebras $R\rightarrow S$ and an ideal simplicial algebra structure on the associated bar construction $Bar(S,R)$. We also explain this structure for crossed squares of algebras.

Keywords

crossed module , crossed square , ideal map

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