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Crossed semimodules and cat$^{\bf 1}$-monoids

Sedat Temel
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2019.06|한국수학논문집 (Korean Journal of Mathematics)|제27권 제2호|pp. 535-545

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참고문헌

키워드

Crossed modulecrossed semimodulecat$^1$-groupcat$^1$-monoid
주제분류수학

초록

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.

Abstract

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.

참고문헌 (31)

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