POINTED HOMOTOPY OF MAPS BETWEEN 2-CROSSED MODULES OF COMMUTATIVE ALGEBRAS
HOMOLOGY HOMOTOPY AND APPLICATIONS, cilt.18, sa.1, ss.99-128, 2016 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 18 Sayı: 1
- Basım Tarihi: 2016
- Doi Numarası: 10.4310/hha.2016.v18.n1.a6
- Dergi Adı: HOMOLOGY HOMOTOPY AND APPLICATIONS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.99-128
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Eskişehir Osmangazi Üniversitesi Adresli: Evet
Özet
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, we construct for maps of 2-crossed modules a homotopy relation, and prove that it yields an equivalence relation in very unrestricted cases (freeness up to order one of the domain 2-crossed module). This latter condition strictly includes the case when the domain is cofibrant. Furthermore, we prove that this notion of homotopy yields a groupoid with objects being the 2-crossed module maps between two fixed 2-crossed modules (with free up to order one domain), the morphisms being the homotopies between 2-crossed module maps.