Geodesic
Equality of maps and coherence theorem for biclosed categories
Zapiski Nauchnykh Seminarov POMI, Theoretical application of methods of mathematical logic. Part III, Tome 105 (1981), pp. 3-9
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The problems in question are reduced here to ones for closed categories solved in [2,3]. First a natural deduction system is constructed and a term is assigned to any derivation. Equivalence relation ($\underset{BC}\equiv$) is defined for terms. Next a term is assigned to every canonical map and it is proved that two canonical maps are equal iff corresponding terms are equivalent. Finally, using the results from [2,3] we present decision algorithm for ($\underset{BC}\equiv$) and prove coherence theorem for canonical maps in ВС categories. 
@article{ZNSL_1981_105_a1,
     author = {A. A. Babaev},
     title = {Equality of maps and coherence theorem for biclosed categories},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {3--9},
     year = {1981},
     volume = {105},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1981_105_a1/}
}
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A. A. Babaev. Equality of maps and coherence theorem for biclosed categories. Zapiski Nauchnykh Seminarov POMI, Theoretical application of methods of mathematical logic. Part III, Tome 105 (1981), pp. 3-9. http://geodesic.mathdoc.fr/item/ZNSL_1981_105_a1/