A note on Penon’s definition of weak n -category. Unicorn Meta Zoo 3: In The Princeton Companion to Mathematics , ed. The argument seems to be well known, although I learned it from these short notes of Tom Leinster. Translating it into the easier language of monoidal bicategories we obtain the following. Imaginary , Berlin July, Invited speaker.
Hence, I am looking for techniques that could simplify working with a general tricategory. A direct proof that the category of 3-computads is not cartesian closed. Non-specialist for non-specialist preprints click here. In Applied Categorical Structures, 15 4: Theory and Applications of Categories 29 , With Nick Gurski,
With Tom Leinster, In Applied Categorical Structures, 15 4: I frequently find it very problematic to prove any uniqueness results due to the relevant computations being difficult. Towards an n-category of cobordisms. In Journal of Pure and Applied Algebra, Eugenia Cheng’s Research papers The category of opetopes and the category of opetopic sets.
Journal of K-Theory, 13 2: How do we grade questions? In Applied Categorical Structures15 4: Here I am using the algebraic definition of a monoidal bicategory, ie. Submitted book Higher dimensional categories: In particular the “naive” version of coherence for monoidal bicategories I asked for above is true.
Slides from talks Terminal coalgebras. Timothy Gowers et al, Princeton University Press, Distributive laws for Lawvere Theories, Also available hereand on the arXiv Theory and Applications of Categories 29 I believe some argument similar in spirit to the one from notes of Tom Leinster should work, but triequivalences or more generally, homomorphisms of tricategories are such complicated objects that it is not quite obvious for me how to do this.
Last updated 3rd October Timothy Gowers et al, Princeton University Press, Has this been covered in the literature? Typelevel SummitOslo 4 May Keynote speaker.
In The Princeton Companion to Mathematicsed. The strictifying version of coherence is an important theorem on its own right, but it also implies the thhesis version of coherence with the following argument. In Journal of Pure and Applied Algebra2: In Journal of Pure and Applied Algebra, 2: Cyclic multicategories, multivariable adjunctions and mates.
A note on Penon’s definition of weak n -category. The question is answered in a paper of Nick Gurski, “An algebraic theory of tricategories” and probably also in his new book “Coherence in Three-dimensional Category Theory”.
Sign up using Facebook. Any tricategory is triequivalent to a Gray -category, ie.
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Cyclic multicategories, multivariable adjunctions and mates. To appear in Algebra Universalis. Unicorn Meta Zoo 3: