We discuss the notion of representable functors in Category Theory. Then, we present Yoneda's lemma and apply it to the situation of group objects in categories and their relation to functors into the category of groups, resulting in a surprising result that these two concepts are essentially the same. Most proofs are included, as well as lots of commutative diagrams.
My name is Felix Fontein and I'm currently a software developer at Dybuster AG. Until February 2014, I used to be a postdoctoral fellow at the University of Zurich. I'm working in the area of Computational Number Theory, in particular on arithmetic in global fields, the infrastructure of such fields, computation of regulators and fundamental units, and related areas. I studied at University of Oldenburg and at the University of Zurich, and was a postdoctoral fellow at the University of Calgary before going back to Zurich.
About This Blog.
This blog focusses on my research as well as other mathematical topics which I am interested in.
- Partial Fractions.
- The Probability That Two Numbers Are Coprime.
- The Power of the Distributive Law.
- A Cute Identity.
- Solving Certain Linear Systems over the Integers.
- On a Certain Determinant.
- A Strange Inequality.
- Multiplicity of the Determinant.
- Rigorous Arithmetic in the Arakelov Divisor Class Group of a Number Field.
baby steps Cayley-Hamliton Chinese Remainder Theorem determinant DLP f-representation finite abelian group function field genus giant steps group functors Hasse derivative Hensel's lemma inequality of arithmetic and geometric mean infrastructure Jordan decomposition linear system of equations Leibniz rule Muirhead's inequality n-dimensional number field one-dimensional probability of being coprime Parseval's identity reduction Rao-Blackwell Theorem tensor product topological argument Taylor's formula universal property