In Applied Categorical Structures, 15 4: In Theory and Applications of Categories, However, coherence for monoidal categories can also refer to the following result: Towards an n-category of cobordisms. Translating it into the easier language of monoidal bicategories we obtain the following.
Submitted book Higher dimensional categories: In Journal of Pure and Applied Algebra, 2: Sign up or log in Sign up using Google. Here I say “simple-minded” to mean that it can be presented as a statement of the form “some diagram commutes”. The argument seems to be well known, although I learned it from these short notes of Tom Leinster.
Any tricategory is triequivalent to a Gray -category, ie. A direct proof that the category of 3-computads is not cartesian closed.
In Theory and Applications of Categories, In Theory and Applications of Categories, To appear in Algebra Universalis. How do we grade questions?
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In particular, any monoidal bicategory is equivalent to a Gray monoid. The category of opetopes and the category of opetopic sets. In Journal of Pure and Applied Algebra, 3: Recall Mac Lane’s version of coherence for monoidal categories, which one can state informally as follows:. For example, is the following naive generalization of Mac Lane coherence true?
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Comparing operadic theories of n -category,47 pages. Towards an n -category of cobordisms.
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Sign up using Facebook. However, what is not clear to me is how to extract from this some “simple-minded” corollaries, ie. Here I say “simple-minded” to mean that it can be presented as a statement of the form “some diagram commutes”. In Journal of Pure and Applied Algebra, I stumbled nicck this type of questions while studying possible definitions of a dual pair of objects in a monoidal bicategory.
I frequently find it very problematic to prove any uniqueness results due to the relevant computations being difficult. The strictifying version of coherence is an important theorem on its own right, but it also implies nck simple-minded version of coherence with the following argument.
In Journal of Pure and Applied Algebra2: Distributive laws for Lawvere Theories, Cyclic multicategories, multivariable adjunctions and mates. Home Questions Tags Users Unanswered.