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 ...

Here Spec(R) is the set of prime ideals p of R, and Frac(R / p) is the field of fractions of the integral domain R / p. In particular, NF(b) is a coproduct of representables for each b ∈ B. (In the ...

Thanks for a really interesting post. I hadn’t heard of Martianus Capella. Whilst Aristotle got the quantified relationship between force and velocity wrong, I happen to like his notion of force in ...

Then show that the passage n ↦ n n \mapsto \mathbf {n} respects addition, multiplication and exponentiation. For example, if we write p = m + n p = m + n then p \mathbf {p} is the coproduct of m ...

The more I read of your notes, the more I wonder if it is really a course in category theory or in set theory. You are certainly teaching a lot of category-theoretic techniques and ideas, even if the ...

In Part 1, I explained my hopes that classical statistical mechanics reduces to thermodynamics in the limit where Boltzmann’s constant k k approaches zero. In Part 2, I explained exactly what I mean ...

Physicists often say things like this: “Special relativity reduces to Newtonian mechanics as the speed of light, c c, approaches ∞ \infty.” “Quantum mechanics reduces to classical mechanics as ...

for each object X, Y, Z X, Y, Z in C \mathcal {C}. These are subject to the following conditions. The simplex category Δ \mathbf {\Delta} and its subcategory Δ⊥ \mathbf {\Delta}_ {\bot} A simple ...

Guest post by C.B. Aberlé and Rubén Maldonado Fibrations are a fundamental concept of category theory and categorical logic that have become increasingly relevant to the world of applied category ...

I wrote a little book about entropy; here’s the current draft: What is Entropy? If you see typos and other mistakes, or have trouble understanding things, please let me know! An alternative title ...

is always an isomorphism. The above definition is justified by the following: Theorem: A multicategory 𝒞 is isomorphic to M (𝒟) for some monoidal category 𝒟 if and only if it is representable. (we ...