are isomorphisms. Definition. A symmetric 2-rig is a 2-rig whose underlying monoidal category is a symmetric monoidal category. One can work through the details of these definitions and show the ...

These are some lecture notes for a 4 1 2 \frac {1} {2} -hour minicourse I’m teaching at the Summer School on Algebra at the Zografou campus of the National Technical University of Athens. To save time ...

The monoid of n × n n \times n matrices has an obvious n n -dimensional representation, and you can get all its representations from this one by operations that you can apply to any representation. So ...

and this is the bar construction applied to X. This description appears in Mac Lane’s Categories for the Working Mathematician, which is where I first learned about it (see section VII.6 in the second ...

Current itex2MML Version: 1.6.1 (10/3/2021) Installation: Readme Source code: (download | browse repository) Here is a list of all the TeX commands currently implemented in itex2MML. Most should be ...

The homotopy coherent nerve By familiar abstract nonsense, the adjunction C ⊣ N \mathbb {C} \dashv \mathbb {N} is uniquely determined by a functor Δ → \rightarrow sSet-Cat, which sends each object [n] ...

Peter Scholze has just published a challenge to the automated mathematical formalisation community in a post – Liquid tensor experiment – on Kevin Buzzard’s blog. Peter explains there the motivation ...

Hello (none)@40.77.167.4. So nice of you to stop by. I'm a member of the Theory Group here at UT. I've been at UT since September 1994. Before coming here, I was an Assistant Professor in the theory ...

as you’d hope for in a categorified ring. From now on I’m going to say ‘2-rig’ when I mean symmetric 2-rig: that is, one where the tensor product is symmetric monoidal. It’s just like how algebraic ...

Why Mathematics is Boring I don’t really think mathematics is boring. I hope you don’t either. But I can’t count the number of times I’ve launched into reading a math paper, dewy-eyed and eager to ...

Thus 01001, or, BRBBR, gives the ace of spades. All you need to do now to perform the card trick is take a pack of cards, throw out all of the nines, the tens and the royals, then order the remaining ...

That is correct. There are finite index subgroups of profinite groups that are not open, i.e., there are profinite groups that do not equal their own profinite completion. However, by definition, the ...