16,774 reputation
14098
bio website andrej.com
location Ljubljana
age 43
visits member for 4 years, 11 months
seen 2 hours ago
I am a professional mathematician. My area of research is logic, constructive and computable mathematics, category theory, and semantics of programming languages.

Sep
25
comment Why so much graph theory?
Wrong forum, but yes all those things have many applications.
Sep
12
revised Is it consistent with ZFC (or ZF) that every definable family of sets has at least one definable member?
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Sep
12
revised Is it consistent with ZFC (or ZF) that every definable family of sets has at least one definable member?
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Sep
12
revised What is the Implicit Function Theorem good for?
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Sep
5
comment What is the spectrum of possible cofinality types for cuts in an ordered field? Or in a model of the hyperreals? Or in a nonstandard model of arithmetic?
My hidden agenda is to get you to use a definition that works constructively, of course.
Sep
5
answered What is the spectrum of possible cofinality types for cuts in an ordered field? Or in a model of the hyperreals? Or in a nonstandard model of arithmetic?
Sep
1
comment Is there a general notion of semigroup action?
ResearchGate is evil. Here is a link to Funk & Hofstra's original article: tac.mta.ca/tac/volumes/24/6/24-06abs.html Any yes, that's an excellent reference!
Sep
1
comment Is there a general notion of semigroup action?
I summon Robin Cockett!
Sep
1
comment Is there a general notion of semigroup action?
Your semigroup and the object live in the same category. Another option is to let semigroup live in the category of sets (or wherever your hom-sets live) and then you can define what it means for such a semigroup to act on an object in a category.
Sep
1
comment Is there a general notion of semigroup action?
So, is your question: "What is the categorical generalization of the theorem which says that every inverse semigroup can be repersented by partial symmetries?" The first part of your new main question is easily answered: yes, it makes sense because every inverse semigroup is a semigroup. For the second question, I need to recall how the partial symmetries thing works...
Aug
31
comment Is the fixed point property for posets preserved by products?
Are you just after nasty counterexamples, or are you also interested in how to make the FPP property well behaved? If the later, see "Complete axioms for categorical fixed point operators" by Alex Simpson and Gordon Plotkin (homepages.inf.ed.ac.uk/als/Research/fixpoints.ps.gz) where they define suitable uniformity conditions for FPP property to behave well.
Aug
30
comment Is there a general notion of semigroup action?
I am in fact downvoting the question because it is unclear what it is asking. Let's continue the discussion.
Aug
30
comment Is there a general notion of semigroup action?
Your question about getting a notion of partial morphism is separate from what makes a semigroup action. For that, I recommed reading: J. Robin B. Cockett, Stephen Lack: Restriction categories I: categories of partial maps. Theor. Comput. Sci. 270(1-2): 223-259 (2002), and also the second paper J. Robin B. Cockett, Stephen Lack: Restriction categories II: partial map classification. Theor. Comput. Sci. 294(1/2): 61-102 (2003)
Aug
30
comment Is there a general notion of semigroup action?
The action of a semigroup $G$ in a category $\mathcal{C}$ is given by a functor $G \to \mathcal{C}$, where we view $G$ as a category with a single object, and the morphisms are the elements of $G$. This comes down to: an action is given by an object $X$ in $\mathcal{C}$ and a semigroup homomorphism $G \to \mathrm{Hom}(X,X)$. It's all completely analogous to group actions, so I don't really understand what you'd like.
Aug
19
revised In the category of sets epimorphisms are surjective - Constructive Proof?
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Aug
19
comment In the category of sets epimorphisms are surjective - Constructive Proof?
It is not really different, but I would say that it is less mysterious.
Aug
18
answered In the category of sets epimorphisms are surjective - Constructive Proof?
Aug
13
comment How to define the input of computable function or Turing machine over real numbers
I specifically preempted my comment with "regarding the question..." so as to make it clear I was not discussing complexity (although what I said still stands, except as you note, things get more complicated). Of course complexity is a very interesting issue. Some work has been done in Type Two Effectivity. Essentially, complexity on a space $X$ makes sense when each point of $X$ has compactly many representatives, see e.g. homepages.inf.ed.ac.uk/als/Research/Others/schroeder-mlq04.pdf
Aug
13
comment How to define the input of computable function or Turing machine over real numbers
No, that is not the point. We can implement the reals, but it's a bit trickier than you'd expect. You cannot naively expect to implement equality as a boolean test, for instance, but you can implement inequality as a semidecidable test. So there are some surprises, and that's why people are so confused about computation over the reals.
Aug
13
comment How to define the input of computable function or Turing machine over real numbers
Regarding the question "what representation of reals do we have to choose", please read my answer at cstheory.stackexchange.com/a/16547/705