TY  - JOUR
T1  - Action of Crossed Modules and Bar Construction
AU  - Ceyran, Emrah
AU  - Ulualan, Erdal
PY  - 2025
DA  - July
Y2  - 2024
DO  - 10.54286/ikjm.1536223
JF  - Ikonion Journal of Mathematics
JO  - ikjm
PB  - Nihat AKGÜNEŞ
WT  - DergiPark
SN  - 2687-6531
SP  - 49
EP  - 61
VL  - 7
IS  - 1
LA  - en
AB  - If a group $N$ acts on a set $X$, a simplicial set $Bar(X,N)$ using the usual bar construction has been provided. In this construction, if the group $N$ acts on a group $G$ via a homomorphism $f:N\rightarrow G$, then $Bar(G,N)$ has a simplicial set structure. In the case of $f$ has a crossed module structure, $Bar(G,N)$ has a normal simplicial group structure.   In this work, by defining an action of a crossed module $\partial: N_1 \longrightarrow X_1$ on a homomorphism of groups $f: N_2 \longrightarrow X_2 $ via a double map $\alpha: \partial\rightarrow f$, we will construct a bisimplicial set,  using the 2-dimensional version  of the usual Bar construction.
KW  - Bar construction
KW  - (Bi)implicial sets
KW  - Crossed modules
KW  - Moore complex.
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UR  - https://doi.org/10.54286/ikjm.1536223
L1  - https://dergipark.org.tr/en/download/article-file/4158053
ER  -