Braided Premonoidal Coherence
نویسنده
چکیده
The constraints of a monoidal category are too strong for some applications in physics. Although the natural isomorphism property is founded on strong physical principles (see Joyce [2]) there are no conclusive grounds for requiring that the pentagon and triangle diagrams hold. For example in Joyce [4,5] recouplings embodying the Pauli exclusion principle are natural isomorphisms that do not satisfy the pentagon diagram for representations of the group SU(n) where n > 2. This provides motivation for investigating weakened monoidal structures. A partial exploration of the problem is given in Joyce [3] and does not consider braids, nor violations of the triangle diagram. An alternative approach using n–categories is given by Yanofsky [10]
منابع مشابه
Coherence for braided and symmetric pseudomonoids
Presentations for unbraided, braided and symmetric pseudomonoids are defined. Biequivalences characterising the semistrict bicategories generated by these presentations are proven. It is shown that these biequivalences categorify results in the theory of monoids and commutative monoids, and are generalisations of standard coherence theorems for braided and symmetric monoidal categories.
متن کاملLax Operad Actions and Coherence for Monoidal N -categories, A∞ Rings and Modules
We establish a general coherence theorem for lax operad actions on an n-category which implies that an n-category with such an action is lax equivalent to one with a strict action. This includes familiar coherence results (e.g. for symmetric monoidal categories) and many new ones. In particular, any braided monoidal n-category is lax equivalent to a strict braided monoidal n-category. We also o...
متن کاملNatural Associativity without the Pentagon Condition
A premonoidal category is equipped only with a bifunctor and a natural isomorphism for associativity. We introduce a (deformation) natural automorphism, q, representing the deviation from the Pentagon condition. We uncover a binary tree representation for all diagrams involving a and q and provide a link to permutations and linear orderings. This leads to other notions of premonoidalness. We de...
متن کاملAn Alternative Description of Braided Monoidal Categories
We give an alternative presentation of braided monoidal categories. Instead of the usual associativity and braiding we have just one constraint (the b-structure). In the unital case, the coherence conditions for a b-structure are shown to be equivalent to the usual associativity, unit and braiding axioms. We also discuss the next dimensional version, that is, b-structures on bicategories. As an...
متن کاملar X iv : m at h / 05 06 60 0 v 13 [ m at h . C T ] 1 6 M ay 2 00 7 Associativity as Commutativity
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 an...
متن کامل