Last updated 3rd October , For example, is the following naive generalization of Mac Lane coherence true? In The Princeton Companion to Mathematics , ed. However, what is not clear to me is how to extract from this some “simple-minded” corollaries, ie. Weak omega-categories via terminal coalgebras. Sign up using Facebook.
Recall Mac Lane’s version of coherence for monoidal categories, which one can state informally as follows:. The category of opetopes and the category of opetopic sets. In The Princeton Companion to Mathematics , ed. In particular, any monoidal bicategory is equivalent to a Gray monoid. Comparing operadic theories of n-category, , 47 pages.
higher category theory – Simple-minded coherence of tricategories – MathOverflow
Unicorn Meta Zoo 3: Translating it into the easier language of monoidal bicategories we obtain the following. The periodic table of n -categories for low dimensions II: What are the possible references? This generalization turns out to be false. Has this been covered in the literature?
Theory and Applications of Categories 29 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.
It has quite a lot beyond what is in Gordon, Street, Power, including making the theory of tricategories fully algebraic. The category of opetopes and the category of opetopic sets.
To appear in Algebra Universalis. Non-specialist for non-specialist preprints click here.
Timothy Gowers et al, Princeton University Press, In particular the “naive” version of coherence for monoidal bicategories I asked for above is true. 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 fhesis to the relevant computations being difficult.
As braiding are in general not symmetries, some diagrams of constraint 2-cells in monoidal bicategories do not commute in general. Post as a guest Name.
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, ImaginaryBerlin July, Invited speaker. I believe some argument similar in spirit nidk the one from notes of Tom Leinster should tehsis, but triequivalences or more generally, homomorphisms of tricategories are such complicated objects that it is not quite obvious for me how to do this.
Comparing operadic theories of n -category,47 pages.
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Weak omega-categories via terminal coalgebras. A note on Penon’s definition of weak n -category. With Nick Gurski, Hence, I am looking for techniques that could simplify working with a general tricategory.
In particular, any monoidal bicategory is equivalent to a Gray monoid. Sign up using Email and Password.