Timothy Gowers et al, Princeton University Press, Is there any general framework for proving that some classes of diagrams commute in every tricategory? Sign up using Email and Password. Eugenia Cheng’s Research papers The category of opetopes and the category of opetopic sets. However, coherence for monoidal categories can also refer to the following result: Recall Mac Lane’s version of coherence for monoidal categories, which one can state informally as follows:. Has this been covered in the literature?
For example, is the following naive generalization of Mac Lane coherence true? With Nick Gurski and Emily Riehl. Is there any general framework for proving that some classes of diagrams commute in every tricategory? Cyclic multicategories, multivariable adjunctions and mates. Sign up or log in Sign up using Google. This is certainly an important and powerful result. In Journal of Pure and Applied Algebra, 2:
Research – Eugenia Cheng
With Aaron Lauda, In Journal of Pure and Applied Algebra, 3: Cyclic multicategories, multivariable adjunctions and mates. Journal of K-Theory13 2: In Journal of Pure and Applied Algebra, Also available hereand on the arXiv Has this burski covered in the literature?
Submitted book Higher dimensional categories: As braiding are in general not symmetries, some diagrams of gurwki 2-cells in monoidal bicategories do not commute in general.
This is related to the fact that a one-object monoidal bicategory is “morally the same” as a braided monoidal category a result due to Gordon, Power, Streetwith the braiding given by a clever composition of 2-cells.
Simple-minded coherence of tricategories Ask Question.
higher category theory – Simple-minded coherence of tricategories – MathOverflow
Comparing operadic theories of n-category,47 pages. In Journal of Pure and Applied Algebra2: ImaginaryBerlin July, Invited speaker. In The Princeton Companion to Mathematicsed. A direct proof that the category of 3-computads is not cartesian closed. Here I say “simple-minded” to mean that it can be presented as a statement of the form “some diagram commutes”. Home Questions Tags Users Unanswered.
College of Arts and Sciences
For example, is the following naive generalization of Mac Lane coherence true? I stumbled upon this type of questions while studying possible definitions of a dual pair of objects in a monoidal bicategory.
Also available hereand on the arXiv The category of opetopes and the category of opetopic sets. A direct proof that the category of 3-computads is not cartesian closed.
In Homotopy, Homology and Applications13 2: However, what is not clear to me is how to extract from this some “simple-minded” corollaries, ie. 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 the simple-minded version of coherence with the following argument. In Journal of Pure and Applied Algebra, 2: Comparing operadic theories of n -category,47 pages. 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.
Unicorn Meta Zoo 3: With Nick Gurski, The periodic table of n-categories for low dimensions II: To appear in Theory and Applications of Categories. Email Required, but never shown.
With Nick Gurski,