POINTED HOMOTOPY OF MAPS BETWEEN 2-CROSSED MODULES OF COMMUTATIVE ALGEBRAS

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AKÇA İ. İ., EMİR K., Martins J. F.

HOMOLOGY HOMOTOPY AND APPLICATIONS, cilt.18, sa.1, ss.99-128, 2016 (SCI-Expanded) identifier identifier

  • 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
  • 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.