- Commit
- 59f4eea9478b9d6311052b0411f04b50cbca6212
- Parent
- b10f1352dfb0b9b52767bed1944bcb716c87d810
- Author
- Pablo <pablo-escobar@riseup.net>
- Date
Added a reference to the concept of adjoint functors
Source code for my notes on representations of semisimple Lie algebras and Olivier Mathieu's classification of simple weight modules
Added a reference to the concept of adjoint functors
2 files changed, 10 insertions, 1 deletion
Status | File Name | N° Changes | Insertions | Deletions |
Modified | references.bib | 8 | 8 | 0 |
Modified | sections/introduction.tex | 3 | 2 | 1 |
diff --git a/references.bib b/references.bib @@ -150,3 +150,11 @@ pages = {985--1021}, year = {1896} } + +@book{maclane, + title = {Categories for the working mathematician}, + author = {Mac Lane, Saunders}, + publisher = {Springer-Verlag}, + year = {1971}, + edition = {6}, +}
diff --git a/sections/introduction.tex b/sections/introduction.tex @@ -638,7 +638,8 @@ It is important to note, however, that \(\mathcal{U} : K\text{-}\mathbf{LieAlg} \(\mathfrak{g} = K\) is the \(1\)-dimensional Abelian Lie algebra then \(\mathcal{U}(\mathfrak{g}) \cong K[x]\), which is infinite-dimensional. Nevertheless, Proposition~\ref{thm:universal-env-uni-prop} may be restated -as\dots +using the language of adjoint functors -- as described in \cite{maclane} for +instance. \begin{corollary} If \(\operatorname{Lie} : K\text{-}\mathbf{Alg} \to