Coderivations of Ranked Bigroupoids

Further Results on Derivations of Ranked Bigroupoids

Several authors 1–4 have studied derivations in rings and near rings. Jun and Xin 5 applied the notion of derivation in ring and near-ring theory to BCI-algebras, and as a result they introduced a new concept, called a regular derivation, in BCI-algebras. Zhan and Liu 6 studied f-derivations in BCI-algebras. Alshehri 7 applied the notion of derivations to incline algebras. Alshehri et al. 8 int...

(n − 1)-Step Derivations on n-Groupoids: The Case n = 3

We define a ranked trigroupoid as a natural followup on the idea of a ranked bigroupoid. We consider the idea of a derivation on such a trigroupoid as representing a two-step process on a pair of ranked bigroupoids where the mapping d is a self-derivation at each step. Following up on this idea we obtain several results and conclusions of interest. We also discuss the notion of a couplet (D, d)...

On the Coderivations of Some Hopf Algebras

Coderivations of Cocommutative Coalgebras

Coalgebraic Approach to the Loday Infinity Category, Stem Differential for 2n-ary Graded and Homotopy Algebras

We define a graded twisted-coassociative coproduct on the tensor algebra TW of any Zn-graded vector space W . If W is the desuspension space ↓V of a graded vector space V , the coderivations (resp. quadratic “degree 1” codifferentials, arbitrary odd codifferentials) of this coalgebra are 1to-1 with sequences πs, s ≥ 1, of s-linear maps on V (resp. Zn-graded Loday structures on V , sequences tha...