We present some formal properties of (symmetrical) commutativity, the major criterion used in transactional systems, which allow us to fully understand its advantages and disadvantages. The main result is that commutativity is subject to the same limitation as compatibility for arbitrary objects. However, commutativity has also a number of attracting properties, one of which is related to recov...

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 degenerat...

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 degenerat...

In the large N c limit, all hyperon decays involving the same quark diagram Q ! Q 0 are described by a single weak form factor QQ 0(w). No assumption on the mass of Q or Q 0 is necessary, making our results applicable to both b ! c and c ! s transitions. This same form factor describes both Q ! Q 0 and () Q ! () Q 0 transitions. The (non-)commutativity between the heavy quark and the large N c ...