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The main idea of this paper is to introduce the notion of cat$^{\bf{1}}$-monoids and to prove that the category of crossed semimodules $ \mathcal{C} = (A,B,\partial) $ where $ A $ is a group is equivalent to the category of cat$^{\bf{1}}$-monoids. This is a generalization of the well known equivalence between category of cat$^{\bf{1}}$-groups and that of crossed modules over groups.
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참고문헌 (31)
참고문헌 신청
Akꠕz, H.F. / 2013 / Coverings of internal groupoids and crossed modules in the category of groups with operations / Geor-gian Mathematical Journal 20(2):223~238
Baez, J. C. / 2004 / Higher Dimensional Algebra V : 2-Groups / Theory and Applications of Categories 12(14):423~491
Baez J.C. / 2009 / The classifying space of a topological 2-group / Al-gebraic Topology Abel Symposia 4:1~31
Baez, J.C. / 2012 / Innite-Dimensional Repre-sentations of 2-Groups / Memoirs of the American Mathematical Society 219(1032)
Brown, R. / 1999 / Groupoids and crossed objects in algebraic topology / Homology Ho-motopy Appl 1:1~78
Baez, J. C. / 2004 / Higher Dimensional Algebra V : 2-Groups / Theory and Applications of Categories 12(14):423~491
Baez J.C. / 2009 / The classifying space of a topological 2-group / Al-gebraic Topology Abel Symposia 4:1~31
Baez, J.C. / 2012 / Innite-Dimensional Repre-sentations of 2-Groups / Memoirs of the American Mathematical Society 219(1032)
Brown, R. / 1999 / Groupoids and crossed objects in algebraic topology / Homology Ho-motopy Appl 1:1~78
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