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After reminding what coherences spaces are and how they interpret linearlogic, we define a modality "flag" in the category of coherence spaces (orhypercoherences) with two inverse linear (iso)morphisms: "duplication" from(flag A) to ((flag A) < (flag A)) and "contraction" in the opposite direction-- where < is the self dual and non-commutative connective known as "before" inpomset logic and known as "seq(ential)" in the deep inference system (S)BV. Inaddition, as expected, the coherence space A is a retract of its modal image(flag A). This suggests an intuitive interpretation of (flag A) as "repeatedlyA" or as "A at any instant" when "before" is given a temporal interpretation.We hope the semantic construction of flag(A) will help to design proof rulesfor "flag" and we briefly discuss this at the end of the paper.

Flag: a Self-Dual Modality for Non-Commutative Contraction and Duplication in the Category of Coherence Spaces