Tim Porter
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Registered User
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I was Professor in Mathematics in the University of Wales, Bangor, until 2005, when they shut the mathematics department down. (Please do not react by saying `a university without a maths department! How is that possible?' The answer is `It is all too easy in some education systems'.)
Since the closure, I have been, amongst other things, a visiting professor/researcher in Ottawa, Galway, Paris, Granada, and have given numerous workshop and seminar talks (Lisbon, Porto, Barcelona, Cardiff, Luminy). I was a CNRS visitor in Lyon (France) working with Philippe Malbos and Yves Guiraud and in autumn last year (2011) visited the Université de Savoie, Chambery on a research visit. Recently I have been visiting Granada for four weeks followed by short visits to Logrono and Madrid. I am an `emeritus member' of WIMCS and helped organise a recent WIMCS related workshop in Cardiff on Higher Gauge Theory, TQFTs and categorification. I am a Fellow of the Learned Society of Wales. |
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May 21 |
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objects which can’t be defined without making choices but which end up independent of the choice @Daniel continued: There is another aspect that this question does not quite ask and that is the question of computability of an object. An object may be defined using a universal property, for instance, but is computed by choosing some presentation. Yet again, for instance, the universal covering space of a space is constructed using a choice of base point, but sometimes one uses all possible base points and works with a covering system, which is a functor on the fundamental groupoid, so is free of choices as it uses all choices of base point. |
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May 21 |
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objects which can’t be defined without making choices but which end up independent of the choice @Daniel: 'but because groupoids are more complicated algebraic objects than groups' They are no more complicated algebraically, since their algebraic theory is the theory of groups but with a certain graph theoretic side to it. Many group theoretic theorems are much easier to prove using groupoids as covering groupoids are so neat to use. @Jeremy: perhaps that suggests that the fundamental group is less fundamental than the fundamental groupoid! Compare Grothendieck's SGA definition of $\pi_1$. Groups are just better known and so are more convenient a lot of the time |
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May 16 |
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Can group cohomology be interpreted as an obstruction to lifts? Have you looked at the homotopy theoretic interpretation of group cohomology? I think therein you will find your answer. |
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May 16 |
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Anomalies in the definition of Turaev’s TQFT Can you add the definition of anomaly (if it is short)? Thanks. |
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May 12 |
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Applications and examples of quotient categories of abelian categories I know and like Stenström's earlier lecture notes, but do not know his book. |
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May 12 |
answered | Applications and examples of quotient categories of abelian categories |
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May 9 |
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A question in category theory ... and not an Argentinian racing pigeon! |
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Apr 29 |
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Generalized Categories for “Higher Homotopy Groupoids” Glad to be of help. |
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Apr 23 |
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Generalized Categories for “Higher Homotopy Groupoids” Let me endorse Ronnie's suggestion. That should help a lot. |
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Apr 23 |
answered | Generalized Categories for “Higher Homotopy Groupoids” |
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Apr 19 |
revised |
Removing a simplicial subset from a simplicial set added 1 characters in body |
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Apr 15 |
answered | Removing a simplicial subset from a simplicial set |
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Apr 3 |
accepted | Presentation of extentions of groups |
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Mar 8 |
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Are there “geometrically nice” sets from which to construct coverings that admit “Vietoris-Rips like” approximations to the nerve? I would disagree with the `well known'. The terms nerve and Cech comlex have a wider and older use than just this. The Wikipedia page is not to be trusted. Vietoris complex is also used in a wider and older meaning for an arbitrary covering. Looking at that Wikipedia entry there are numerous inaccuracies. The Cech complex is not dependent on the embedding. Secondly what do you mean by`other classes of sets'? Have you investigated Dowker's paper on the homology of relations? |
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Jan 29 |
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In your opinion, what are the relative advantages of n-fold categories and n-categories? Adding to Ronnie's comment on crossed n-cubes of groups. These are very very easy to define and give models for homotopy n+1-types. The corresponding n+1-groupoid will have a lot of seemingly extra structure whose details are not that clear once you get to n= 4. The reason, intuitively, is that the crossed n-cube lays things out for you, but at the cost of a lot of repetition of the information, while the n-category folds it all into a small space, so naturally things interact in an apparently more complex way. |
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Jan 25 |
accepted | ANR Subsets of banach spaces |
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Jan 24 |
awarded | ● Yearling |
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Dec 24 |
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The origin of sets? Adam of Balsham was Bishop of St Asaph in Clwyd, North Wales, so not only was a North Walian the first to have used the Greek letter pi for pi (if you see what I mean), but also provided an early set theorist! (I suppose he commuted between Paris and St Asaph! :-)) |
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Dec 21 |
answered | Numerable covers from the point of view of Grothendieck topologies |
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Dec 19 |
answered | Multigraphs and Social Network Analysis |
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Dec 17 |
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A category with objects that are not based on sets or classes As someone else pointed out in the usual DEFINITION of a category you are required to have a SET of morphisms between objects, so from that point of view, your search is DOOMED! If you take a different `foundation' for mathematics, what one do you want? You can follow Lawvere's idea of using categories as the basic things from which to build things... note this is not a foundational exercise as such, rather a pragmatic one. Here is an idea: take categories as basic, then the 2-category of categories (no size to be mentioned since set theory is `anathema') and functors might pass must. :-) |
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Dec 17 |
revised |
A category with objects that are not based on sets or classes deleted 1 characters in body |
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Dec 17 |
answered | A category with objects that are not based on sets or classes |
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Dec 15 |
answered | This is not a category. What is it? |
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Dec 6 |
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Conjectures in Grothendieck’s “Pursuing stacks” I second Todd's point. |
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Dec 6 |
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Conjectures in Grothendieck’s “Pursuing stacks” I should add that Grothendieck's conjectures are often informally stated, and he sometimes suggests that deciding what the theory should look like, and therefore what the conjectures are, is the greater part of the battle for the development of any theory. |
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Dec 6 |
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Conjectures in Grothendieck’s “Pursuing stacks” I have just gone into the n-Lab and have tried to change the wording to reflect Jonathan's very valid points. I have only added a little and changed a little, but would suggest that the entry does need some more work. Does any one have typed out a table of contents of PS? Then linked comments with the future development would of the main themes might be useful. |
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Dec 6 |
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Covering maps in real life that can be demonstrated to students Ronnie, you beat me to it!;-) |
