On the Barr exactness property of $\mathsf{BXMod/R}$
In this work, it is shown that the category $\mathsf{BXMod/R}$ of braided crossed modules over a fixed commutative algebra $R$ is an exact category in the sense of Barr.
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arXiv subjects
Ummahan Ege Arslan
Publications and source records attributed to Ummahan Ege Arslan.
Categorification of Algebras: 2-Algebras
This paper introduces a categorification of $k$-algebras called 2 -algebras, where k is a commutative ring. We define the 2-algebras as a 2-category with single object in which collections of all 1-morphisms and all 2-morphisms are k-algebras. It is shown that the category of 2 -algebras is equivalent to the category of crossed modules in commutative k -algebras. Also we define the notion of homotopy for 2-algebras and we explore the relations of crossed module homotopy and 2-algebra homotopy.
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(Co)-Induced Two Crossed Modules
We introduce the notion of an induced 2-crossed module, which extends the notion of an induced crossed module (Brown and Higgins).
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The Embedding Theorem
In this work, it is shown that the category XMod/P of crossed modules over fixed group P is an exact category and the complete proof of the embedding theorem of XMod/P into a set valued functor category is given.
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Categorical Results in the Theory of Two-Crossed Modules of Commutative Algebras
In this paper we explore some categorical results of 2-crossed module of commutative algebras extending work of Porter in [18]. We also show that the forgetful functor from the category of 2-crossed modules to the category of k-algebras, taking {L, M, P, \partial_2, \partial_1} to the base algebra P, is fibred and cofibred considering the pullback (coinduced) and induced 2-crossed modules constructions, respectively. Also we consider free 2- crossed modules as an application of induced 2-crossed modules.
math.CT↗