10 citations · 23 across the 9 of their papers we have counts for
6 papers · 1 filter
Braided Hopf Crossed Modules Through Simplicial Structures
Kadir Emir, Jan Paseka
Any simplicial Hopf algebra involves different projections between the Hopf algebras for each . The word projection, here meaning a tuple $\partial \co…
The Moore Complex of a Simplicial Cocommutative Hopf Algebra
Kadir Emir
We study the Moore complex of a simplicial cocommutative Hopf algebra through Hopf kernels. The most striking result to emerge from this construction is the coherent definition of…
Limits in Modified Categories of Interest
Kadir Emir, Selim Çetin
We firstly prove the completeness of the category of crossed modules in a modified category of interest. Afterwards, we define pullback crossed modules and pullback cat-objects…
From Simplicial Homotopy to Crossed Module Homotopy in Modified Categories of Interest
Kadir Emir, Selim Çetin
We address the (pointed) homotopy of crossed module morphisms in modified categories of interest; which generalizes the groups and various algebraic structures. We prove that, the…
Two-Fold Homotopy of 2-Crossed Module Maps of Commutative Algebras
İ. İlker Akça, Kadir Emir, João Faria Martins
We address the homotopy theory of 2-crossed modules of commutative algebras. In particular, we define the concept of a 2-fold homotopy between a pair of 1-fold homotopies connectin…
Pointed Homotopy of Maps Between 2-Crossed Modules of Commutative Algebras
İ. İlker Akça, Kadir Emir, João Faria Martins
We address the homotopy theory of 2-crossed modules of commutative algebras, which are equivalent to simplicial commutative algebras with Moore complex of length two. In particular…