Associativity as Commutativity Export

@misc{citeulike:248987, abstract = {It is shown that coherence conditions for monoidal categories concerning associativity are analogous to coherence conditions for strict symmetric monoidal categories, where associativity arrows are identities. Mac Lane's pentagonal coherence condition for associativity is decomposed into conditions concerning commutativity, among which we have a condition analogous to naturality and a degenerate case of Mac Lane's hexagonal condition for commutativity. The pentagon is reduced to an inductive definition of a kind of commutativity.}, archivePrefix = {arXiv}, author = {Dosen, K. and Petric, Z.}, citeulike-article-id = {248987}, citeulike-linkout-0 = {http://arxiv.org/abs/math.CT/0506600}, citeulike-linkout-1 = {http://arxiv.org/pdf/math.CT/0506600}, day = {5}, eprint = {math.CT/0506600}, keywords = {associativity, category, coherence, cut, pnc, prootheory, substitution}, month = {Jul}, posted-at = {2005-08-16 11:55:22}, priority = {2}, title = {Associativity as Commutativity}, url = {http://arxiv.org/abs/math.CT/0506600}, year = {2005} }

TY - ELEC ID - citeulike:248987 L3 - citeulike-article-id:248987 N2 - It is shown that coherence conditions for monoidal categories concerning associativity are analogous to coherence conditions for strict symmetric monoidal categories, where associativity arrows are identities. Mac Lane's pentagonal coherence condition for associativity is decomposed into conditions concerning commutativity, among which we have a condition analogous to naturality and a degenerate case of Mac Lane's hexagonal condition for commutativity. The pentagon is reduced to an inductive definition of a kind of commutativity. TI - Associativity as Commutativity KW - associativity KW - category KW - coherence KW - cut KW - pnc KW - prootheory KW - substitution AU - Dosen, K AU - Petric, Z PY - 2005/Jul/05/ UR - http://arxiv.org/abs/math.CT/0506600 ER -