Two-fold homotopy of 2-crossed module maps of commutative algebras

Akça İ. İ., Emir K., Martins J.

COMMUNICATIONS IN ALGEBRA, cilt.47, sa.1, ss.289-311, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 47 Sayı: 1
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1080/00927872.2018.1476523
  • Dergi Adı: COMMUNICATIONS IN ALGEBRA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.289-311
  • Anahtar Kelimeler: 2-crossed module of commutative algebras, crossed module of commutative algebras, quadratic derivation, simplicial commutative algebra, POINTED HOMOTOPY, HOMOLOGY
  • Eskişehir Osmangazi Üniversitesi Adresli: Evet

Özet

We address the homotopy theory of 2-crossed modules of commutative algebras. In particular, we define the concept of a two-fold homotopy between a pair of one-fold homotopies connecting 2-crossed module maps . We also prove that if the domain 2-crossed module is free up to order one (i.e., if the bottom algebra is a polynomial algebra) then we have a 2-groupoid of 2-crossed module maps and their homotopies and two-fold homotopies.