TY - JOUR TI - Crossed modules bifibred over k-Algebras AB - In this paper we examine on a pair of adjoint functors (πœ™βˆ— , πœ™βˆ—)for a subcategory of the category of crossed modules over commutative algebras where πœ™βˆ—: XMod/𝑃 β†’ XMod/ Q, induced, and πœ™βˆ—: XMod/Q β†’ XMod/𝑃, pullback (co-induced), which enables us to move from crossed 𝑄-modules to crossed P-modules by an algebra morphism πœ™ : P β†’ Q. We show that this adjoint functor pair (πœ™βˆ—, πœ™βˆ—) makes 𝑝 ∢ XMod β†’ k-Alg into a bi- fibred category over k-Alg, the category of commutative algebras, where p is given by 𝑝(𝐢, 𝑅, πœ•) = 𝑅. Also, we give some examples and results on induced crossed modules in the case when πœ™ is an epimorphism or the inclusion of an ideal. AU - GÜRMEN ALANSAL, Γ–zgΓΌn AU - EGE ARSLAN, UMMAHAN DO - 10.17776/csj.727906 PY - 2021 JO - Cumhuriyet Science Journal VL - 42 IS - 1 SN - 2587-2680 SP - 99 EP - 114 DB - TRDizin UR - http://search/yayin/detay/1120636 ER -