In Journal of Pure and Applied Algebra, Timothy Gowers et al, Princeton University Press, My question concerns known results about such “simple-minded” coherence for monoidal bicategories ie. With Aaron Lauda, 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.

Home Questions Tags Users Unanswered. Comparing operadic theories of n-category, , 47 pages. What are the possible references? By using our site, you acknowledge that you have read and understand our Cookie Policy , Privacy Policy , and our Terms of Service. 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”. In Theory and Applications of Categories, 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.

I stumbled upon this type of questions while studying possible definitions of a dual pair of objects in a monoidal bicategory.

To appear in Algebra Universalis. A note on Penon’s definition of weak n -category. This generalization turns out to be false. Comparing operadic theories of n -category,47 pages. Distributive laws for Lawvere Theories, In Journal of Pure and Applied Algebra, To appear in Theory and Applications of Gueski.

# Research – Eugenia Cheng

Submitted book Higher dimensional categories: Translating it into the easier language of monoidal bicategories we obtain the following. Journal of K-Theory13 2: Also available hereand on the arXiv In Journal of Pure and Applied Algebra, 3: With Aaron Lauda, Slides from talks Terminal coalgebras.

For example, is the following naive generalization of Mac Lane coherence true? Timothy Gowers et al, Princeton University Press, With Nick Gurski and Emily Riehl. Recall Mac Lane’s version of coherence for monoidal categories, which one can state informally as follows:.

Post as a guest Nico. 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.

## College of Arts and Sciences

Recall that coherence for tricategories as proved by Gordon, Street, Power has the following form:. With Aaron Lauda, gurxki How do we grade questions?

Cyclic multicategories, multivariable adjunctions and mates. By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. However, what is not clear to me is how to extract from this some “simple-minded” corollaries, gursli.

The periodic table of n-categories for low dimensions II: Has this been covered in the literature? The argument seems to be nidk known, although I learned it from these short notes of Tom Leinster.

In Journal of Pure and Applied Algebra, 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. Sign up using Facebook. Towards an n-category of cobordisms. In Homotopy, Homology and Applications, 13 2: Simple-minded coherence of tricategories Ask Question.