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location Münster, Germany
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I am interested in the interactions between algebraic geometry and category theory. More specifically, I "model" algebraic geometry on cocomplete symmetric monoidal categories.

Here is a link to my PhD thesis. Comments are welcome.

Email: [my last name] [at] uni-muenster.de


14h
comment (co)limits in the category of diffeological spaces vs. category of smooth manifolds
@user59001: Why do you post this on mathoverflow after having received an answer on math.stackexchange? Could you please at least leave a comment there?
2d
awarded  Popular Question
Apr
14
comment Sexy vacuity …
Oups, I meant continuous functions into discrete spaces, aka locally constant functions.
Apr
8
comment Do hom-sets really live in the category Set?
I just wanted to remark that I've posted an answer on the math.SE version of this question.
Mar
30
comment Why is a topology made up of 'open' sets?
"the category of topological spaces is equivalent to the category of relational algebras for the ultrafilter monad." -- they are isomorphic, I guess.
Mar
30
comment Why is a topology made up of 'open' sets?
This great answer reminds me of several "unbiased" or "monadic" definitions of structures such as monoids or monoidal categories. The definition of a monoid "should" really introduce $n$-fold products for $n \in \mathbb{N}$, not just $0$-fold and $2$-fold products. Curiously, the monoid axioms are quite easy to state for $n$-fold products; this is even more true for the coherence axioms in the definition of a monoidal category via $n$-fold tensor products.
Mar
27
revised Notation: Categories of measur(abl)e spaces
added 634 characters in body
Mar
26
awarded  Good Question
Mar
26
comment Notation: Categories of measur(abl)e spaces
Actually $\mathsf{Bor}$ looks really good. But then it's still open how to denote the category of measure spaces. (Or the category of measure spaces equipped with a $\sigma$-ideal, as suggested by Dmitri Pavlov.)
Mar
26
awarded  Enlightened
Mar
26
awarded  Nice Answer
Mar
25
comment Is there an introduction to probability theory from a structuralist/categorical perspective?
One can talk about a field without having to write it down as a tuple. Just say $K$ is the field, an object of the category of fields and not of the category of sets, and don't confuse it with its underlying set $|K|$. Similarly, we can talk about graphs without having to think of them as pairs of sets. The answer claims that it is somehow difficult or distracting to define graphs that way, but I don't agree with this either.
Mar
25
comment Is there an introduction to probability theory from a structuralist/categorical perspective?
By the way, I disagree with Rudin's comment. It basically says "It is a tradition to ignore forgetful functors, so I will follow this tradition" and "argues" for this procedure by saying that otherwise one would "have to" imagine the reals as a quadruple. No. It is really about the question in which category one works. There is a field of real numbers, there is a measure space of real numbers, there is a topological space of real numbers, etc., and it is very unfortunate that all are denoted by the same symbol. At least, one should not forget the forgetful functors between these categories.
Mar
25
comment Is there an introduction to probability theory from a structuralist/categorical perspective?
"probability theory is not about probability spaces" --- yes, but it is perhaps about the category of probability spaces and measurable maps. Random variables are morphisms in that category. The approach to look at families of random variables to understand some distribution is really in the spirit of the Yoneda Lemma. Morphisms are more important than objects.
Mar
25
comment Notation: Categories of measur(abl)e spaces
Thank you! I didn't know this alternative terminology. "measurable space" seems to be more modern than "Borel space". Is this correct?
Mar
25
comment Notation: Categories of measur(abl)e spaces
@JohannesHahn: Yes, I would also call it the (general) 'transformation formula'.
Mar
25
revised Notation: Categories of measur(abl)e spaces
added 519 characters in body
Mar
25
comment Notation: Categories of measur(abl)e spaces
@DmitriPavlov: Thank you for your comment. I have found several papers on measure theory and probability theory which apply category theory to the categories of measurable resp. probability spaces. Do you say that it is hard to do nontrivial measure theory with these categories, but that it is possible for other categories, or that category theory is not useful for nontrivial measure theory at all? In the former case, I would like to know which alternative categories are more suitable.
Mar
25
comment Notation: Categories of measur(abl)e spaces
What do you think about $\mathsf{Measure}$ for the category of measure spaces (and $\mathsf{Meas}$ for the category of measurable spaces)?
Mar
24
comment Notation: Categories of measur(abl)e spaces
@MichaelGreinecker: Thanks! The authors even say "This gives a category which is often called $\mathsf{Meas}$.". So it should be common. Have you seen a notation for the other category?