It is shown that coherence conditions for monoidal categories concerning associativity are analogous to coherence conditions for symmetric 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 degener...

It is shown that coherence conditions for monoidal categories concerning associativity are analogous to coherence conditions for symmetric 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 degener...

We present preliminary simulation results for QED in a non-commutative 4d space-time, which is discretized to a fuzzy lattice. Its numerical treatment becomes feasible after its mapping onto a dimensionally reduced twisted Eguchi-Kawai matrix model. In this formulation we investigate the Wilson loops and in particular the Creutz ratios. This is an ongoing project which aims at non-perturbative ...

It is shown that all the assumptions for symmetric monoidal categories flow out of a unifying principle involving natural isomorphisms of the type (A ∧B) ∧ (C ∧D) → (A ∧ C) ∧ (B ∧D), called medial commutativity. Medial commutativity in the presence of the unit object enables us to define associativity and commutativity natural isomorphisms. In particular, Mac Lane’s pentagonal and hexagonal coh...

We present a technique for automatically generatingcommutativity conditions from (abstract-level) data-structurespecifications. We observe that one can pose the commutativityquestion in a way that does not introduce additional quantifiers,via a mechanized lifting of a (potentially partial) specificationto an equivalent total specification. We then describe an al-gorithm ...

Torgerson’s (1961) conjecture that subjects cannot meaningfully distinguish perceptual ratios and differences has triggered a continuing debate in psychophysics on what constitutes adequate scaling methodology. It is shown that an axiomatic theory of magnitude estimation proposed by Narens (1996, 1997) sheds new light on this problem by dropping the assumption that subjects can report sensation...

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...