2,630 reputation
1628
bio website jakitoimgeisterhaus.blogspot.…
location Munich, Germany
age 37
visits member for 2 years, 10 months
seen 1 hour ago

My past research interests included differential algebraic equations, nonlinear analysis and relations between symmetries and structural properties.

I recently investigated hierarchical structures, starting from group cohomology, continuing with semi-group theory and ending with lattices and universal algebra.


Mar
11
revised Are these adjoint functors to/from the category of monoids with semigroup homomorphisms?
added 2 characters in body
Mar
10
comment Are these adjoint functors to/from the category of monoids with semigroup homomorphisms?
@MartinBrandenburg At least I tried to check that $F(g\circ f)=F(g)\circ F(f)$ for $G_H$. (However, I was wrong, as I figured out now.) I didn't even try to check this for $G_O$... It fails, because $g$ might map the identity element to a "false" identity element, so that $G_O(g\circ f)$ would map the newly adjoint identity element to the identity element, but $G_O(g)\circ G_O(f)$ maps the newly adjoint identity element to a "false" identity element.
Mar
9
asked Are these adjoint functors to/from the category of monoids with semigroup homomorphisms?
Mar
7
comment Can the actual scope of “lattice theory” be summarized as “algebraic order theory”?
@WilliamDeMeo I mean by "scope" how I would tag an article, whether I would present it on a lattice theory conference, publish it in a lattice theory journal, or search in lattice theory publications for related information. My concrete concern is single sorted formal concept analysis, motivated by the answer to a question about the concept lattice.
Mar
6
asked Can the actual scope of “lattice theory” be summarized as “algebraic order theory”?
Feb
8
comment Unifying concepts in mathematics
If I were to write an answer, it would go something like this: Mathematics is as much about teaching and communication of knowledge than about the knowledge itself. Mathematics should not to be confused with an IQ test. The aspect of creation of new domain specific languages should not be underestimated. Also take into account that the greeks used sketches as an integral part of the communication, and that mathematics might once again decide to use additional media as part of the language, in addition to pure words. Take the commutative diagrams of category theory as an example.
Feb
8
comment Unifying concepts in mathematics
Community wiki?
Feb
5
comment Which of these constructions are left adjoints?
These adjunctions are also adjunctions between $\mathsf{PreOrd}$ and $\mathsf{Set}$. All functors factor through the adjoint functors between $\mathsf{Cat}$ and $\mathsf{PreOrd}$. Only $D \dashv Ob$ is a "genuinely new" adjunction between $\mathsf{Set}$ and $\mathsf{Cat}$, because the corresponding functors between $\mathsf{PreOrd}$ and $\mathsf{Cat}$ are not adjoint in the same sense.
Feb
3
revised Why are so many of the oldest unsolved problems in mathematics about number theory?
The objects are certain subsets of natural numbers, not the natural numbers themselves.
Feb
3
answered Why are so many of the oldest unsolved problems in mathematics about number theory?
Feb
3
revised Which of these constructions are left adjoints?
Removed additional question, in order to mark the question as answered. Also removed "forgetful", because it means to forget additional structure, not special properties.
Feb
3
accepted Which of these constructions are left adjoints?
Feb
2
revised Which of these constructions are left adjoints?
I meant left adjoint, i.e. the typical adjoint functor to a forgetful functor. I even tried to work it out before asking whether I meant left or right, but I better should have just looked at some worked out examples.
Feb
2
asked Which of these constructions are left adjoints?
Feb
1
answered Mystified by construction of “group extension” $\{G, T\}$ in Herstein's “Topics in Algebra”
Jan
30
revised Relation between concept lattice and Dedekind–MacNeille completion
I finally understood many valued contexts and contextual scaling. They are the pragmatic solution to my initial problem.
Jan
24
reviewed Approve suggested edit on Cauchy's Integral Theorem
Jan
23
comment Mathematical logic book with answers to exercises
What language would you prefer?
Jan
22
revised Relation between concept lattice and Dedekind–MacNeille completion
deleted 1 characters in body
Jan
22
accepted Relation between concept lattice and Dedekind–MacNeille completion