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Results tagged with ct.category-theory
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user 18702
Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.
1
vote
Is there a name for (pre)sheaves satisfying this transitivity condition?
I am not well-versed in these matters, but I believe Olivia Caramello uses something like this in her toposical formulation of Galois theory. See her paper and, if you can understand French, this brie …
- 1,838
13
votes
2
answers
1k
views
What is the universal property of the Weyl group?
If $G$ is a group and $H\le G$ a subgroup, let $NH$ denote the normalizer of $H$ in $G$, and let $WH = NH/H$; following May's Concise Course, §3.4 this I call the Weyl group. I have also seen the defi …
- 1,838
9
votes
2
answers
474
views
Algebras in a bicategory of spans
$
\newcommand{\Span}{\mathbf{Span}}
\newcommand{\cE}{\mathcal E}
$Given a category $\cE$ with plenty of limits, let $\Span(\cE)$ denote the bicategory of spans in $\cE$. It is known that monads in $\S …
- 1,838
6
votes
Functor category's objects fail to be a class?
This can be circumvented (to some degree) if we use Grothendieck universes instead of classes. Roughly speaking, a set $\mathcal U$ is a universe if it's closed under all the operations we use in ZF. …
- 1,838
2
votes
2
answers
264
views
Automorphisms and Bicategories
Sorry if this isn't the right place for this, it hasn't gotten any answers on ME. I'm reading Lang's section on field theory and he stresses that, unlike typical "universal" constructions which are de …
- 1,838
3
votes
2
answers
741
views
Localization of symmetric monoidal category
Let $\mathcal M$ be a symmetric monoidal category, $S\subset \mathcal M$ a collection of objects and morphisms. I would like to construct the localization $\mathcal M \mathop{\longrightarrow}^T \mathc …
- 1,838
11
votes
4
answers
2k
views
Embedding Theorem for topological spaces, and in general
There are many examples throughout mathematics of abstracting the formal properties of a "familiar" structure, but then having a theorem stating that all models of the abstract axioms embed into one o …
- 1,838