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We introduce the notion of pre-weight structure on a triangulated categoryand study the corresponding pseudo-identities. We propose the notion ofcanonical derived equivalence between algebras that are not necessarily flat,which is associated to a tilting complex. In the flat situation, canonicalderived equivalences coincide with standard derived equivalences in the senseof Rickard. We prove that any derived equivalence starting from a hereditaryalgebra is canonical. The key tool is a general factorization theorem: anyderived equivalence is uniquely factorized as a pseudo-identity followed by acanonical derived equivalence.

Pre-weight structures, pseudo-identities and canonical derived equivalences