Associativity as Commutativity Export

@misc{citeulike:1304594, abstract = {It is shown that coherence conditions for monoidal categories concerning associativity are analogous to coherence conditions for symmetric or braided strictly 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. This decomposition is analogous to the derivation of the Yang-Baxter equation from Mac Lane's hexagon and the naturality of 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 = {1304594}, citeulike-linkout-0 = {http://arxiv.org/abs/math/0506600}, citeulike-linkout-1 = {http://arxiv.org/pdf/math/0506600}, day = {16}, eprint = {math/0506600}, keywords = {algebra, category-theory, mathematics}, month = {May}, posted-at = {2007-05-18 03:56:46}, priority = {2}, title = {Associativity as Commutativity}, url = {http://arxiv.org/abs/math/0506600}, year = {2007} }

TY - ELEC ID - citeulike:1304594 L3 - citeulike-article-id:1304594 N2 - It is shown that coherence conditions for monoidal categories concerning associativity are analogous to coherence conditions for symmetric or braided strictly 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. This decomposition is analogous to the derivation of the Yang-Baxter equation from Mac Lane's hexagon and the naturality of commutativity. The pentagon is reduced to an inductive definition of a kind of commutativity. TI - Associativity as Commutativity KW - algebra KW - category-theory KW - mathematics AU - Dosen, K AU - Petric, Z PY - 2007/May/16/ UR - http://arxiv.org/abs/math/0506600 ER -