Abstract proof structures in multiplicative linear logic are graphs with some additional structure, and the class of proof nets is an inductively defined subclass. F. M'etayer established a correctness criterion by defining homology groups for proof structures, which characterize the proof nets among these. Using this result, we will present a completely algebraical proof of the traditional Contraction Criterion, due to Danos and Regnier. 1 Preliminaries 1.1 MLL The set of formulas of multiplicative linear logic (MLL) is defined as the smallest set containing atoms p 1 ; p 2 ; : : : and their formal negations p ? 1 ; p ? 2 ; : : : , and closed under the binary operations\Omega (tensor) and & (par ). Unary negation is defined by the (commutative) De Morgan laws, i.e. (a\Omega b) ? := a ? & b ? , etc. Derivable objects are sequents ) X, where X is a multiset of formulas. The rules of MLL read: axiom ) a ? ; a cut-rule ) X; a ) a ? ; Y ) X;Y tensor-rule ) X; a ) b; ...