Cyclic multicategories, multivariable adjunctions and mates. Here I say “simple-minded” to mean that it can be presented as a statement of the form “some diagram commutes”. A direct proof that the category of 3-computads is not cartesian closed. Email Required, but never shown. With Tom Leinster, Simple-minded coherence of tricategories Ask Question.
Towards an n-category of cobordisms. Timothy Gowers et al, Princeton University Press, Has this been covered in the literature? With Tom Leinster, Recall that coherence for tricategories as proved by Gordon, Street, Power has the following form:. Also available here , and on the arXiv For example, is the following naive generalization of Mac Lane coherence true?
This generalization turns out to be false. However, coherence for monoidal categories can also refer to the following result: A note nici Penon’s definition of weak n -category. In Homotopy, Homology and Applications, 13 2: The category of opetopes and the category of opetopic sets.
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In Journal of Pure and Applied Algebra3: However, what is not clear to me is how to extract from this some “simple-minded” corollaries, ie. With Aaron Lauda, The periodic table of n-categories for low dimensions II: Email Required, but never shown.
Non-specialist for non-specialist preprints click here. Theory and Applications of Categories 29 In Journal of Pure and Applied Algebra, 3: Any tricategory is triequivalent to a Gray -category, ie. With Tom Leinster, Here I say “simple-minded” to mean that it can be presented as a statement of the form “some diagram commutes”.
In Applied Categorical Structures15 4: What are the possible references? In Thexis, Homology and Applications13 2: Also available hereand on the arXiv Cyclic multicategories, multivariable adjunctions and mates.
With Aaron Lauda, Towards an n -category of cobordisms. The argument seems to be well known, although I learned it from these short notes of Tom Leinster.
I frequently find it very problematic to prove any uniqueness results due to the relevant computations being difficult. Journal of K-Theory13 2: In Journal of Pure and Applied Algebra, In The Princeton Companion to Mathematicsed.
I stumbled upon this type of questions while studying possible definitions of a dual pair of objects in a monoidal bicategory. In particular the “naive” version of coherence for monoidal bicategories I asked for above is true.
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Hence, I am looking for techniques that could simplify working with a general tricategory. Translating it into the easier language of monoidal bicategories we obtain the following.