1 Jul 2009 09:03

### Postdoc and PhD position in Coalgebraic Logic

The EPSRC grant Coalgbraic Logic: Expanding the Scope' is a joint
project between Alexander Kurz (Leicester) and Achim Jung (Birmingham),
seeking to employ a Postdoc in Leicester and a PhD student in Birmingham.

The deadline to apply for the Postdoc position is 22 July 2009.

The advert for the Postdoc position follows.

===

Applications are invited for a Research Associate to work with Dr.
Alexander Kurz (Leicester) and Prof. Achim Jung (Birmingham) on the
EPSRC-funded project Coalgebraic Logic: Expanding the Scope'.

Coalgebraic Logic aims at a uniform theory of transition systems
(coalgebras) and their (typically modal) logics. Central notions are
bisimilarity, co-induction, and initial and final semantics. Coalgebraic
Logic is a young and quickly developing field closely related to areas
such as domain theory, modal logic, Stone duality in mathematics and to
program semantics, concurrency, process algebra in computer science.

The aim of the project is to expand the state of the art in Coalgebraic
Logic in 3 directions: (1) From modal logic to first-order logic; (2) to
study axiomatically defined classes of coalgebras; (3) explore the
relationship with domain theory and extend the expressiveness of logics
obtained via Domain Theory in Logical Form.

Applicants should have or be nearing completion of a PhD in an area


1 Jul 2009 17:43

### realized by fibrations

Suppose I have a sequence of (topological) operads or monads

O \to P \to Q

such that all'  corresponding representations in Top

X \to Y \to Z

are fibrations

is this enough to tell us

O \to P \to Q is a fibration?

jim

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3 Jul 2009 10:37

Dear colleagues,

An Advanced Course on Topological Quantum Field Theories will take place
at the University of Almería from October 19th to 23rd, 2009.

This course aims to engage PhD students and postdoctoral researchers in
these new developments together with international experts in the field.
Lectures will be given by:

* Joachim Kock (Universitat Autònoma de Barcelona)
* Andrey Lazarev (University of Leicester)
* Gregor Masbaum (Institut de Math. de Jussieu / Université Paris
Diderot, Paris 7)
* Christoph Schweigert (Universität Hamburg)

There will be a limited number of grants covering travel and lodging
expenses for young participants.

The course will be followed by the XVI Spanish Topology Meeting from
October 23rd to 24th, 2009.

The organizing committee is looking forward to meeting you soon in Almería.

David Llena (U. Almería)
Fernando Muro (U. Barcelona)
Frank Neumann (U. Leicester)


3 Jul 2009 13:02

### PhD place Available


Dear All,

Do any of you know a student who wants to do a PhD? We have a place
available for anyone interested in type theory, category theory of
functional programming. The student must a first class degree or
masters with distinction

All the best
Neil

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5 Jul 2009 22:54

### Re: separable locale

Dear Thomas,

I'm pretty sure that what Michael meant by "separable" was what
most topologists would call "second countable" -- i.e., countably
generated as a frame. (There are some topology textbooks in which
this condition is called "completely separable".)

Peter Johnstone
---------------------------------
On Tue, 30 Jun 2009, Thomas Streicher wrote:

> Recently rereading Fourman's "Continuous Truth" I came across the term
> "separable locale" but could nowhere find an explanation. Does it mean a
> cHa A for which there exists a countable subset B such that ever a in A is
> the supremum of those b in B with b leq a. This would be the point free
> account of "second countable", i.e. having a countable basis.
> Of course, second countable T_) spaces are separable, i.e. have a
> countable
> dense set.
> Is this reading the "usual" one?
>
> Thomas
>

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6 Jul 2009 10:08

### Non-free cocompletions

Vaughan Pratt writes

> Incidentally, of what use are non-free cocompletions?  Is there any
reason not to define "cocompletion" to make it free?

I can indicate two important uses of non-free cocompletions, and more
precisely cocompletions for particular classes of diagrams preserving
some given colimits:

1. The construction of what, with Charles, we called the "prototype"
and the "type" associated to a sketch (in "Categories of sketchd
structures", Cahiers Top. et Geom. Diff. III-2, 1972)

2. The "complexification process" which, with Jean-Paul Vanbremeersch,
we use extensively in our model for hierarchical evolutionary systems
("Memory Evolutive Systems: Hierarchy, Emergence, Cognition", Elsevier
2007)

Kindly
Andree

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6 Jul 2009 02:31

### Re: Yoneda Theorem < Yoneda Lemma < Dense Yoneda Theorem

On Sun, Jun 28, 2009 at 11:11 PM, Vaughan Pratt<pratt <at> cs.stanford.edu> wrote:
> (Incidentally, of what use are non-free cocompletions?  Is there any
> reason not to define "cocompletion" to make it free?  I seem to recall
> people being happy to drop "free" in this context.  Who ordered "free"?)

To me the unadorned word "completion" connotes an idempotent operation,
which the free (co)completion of a category is not.  A more precise term
would be "free cocomplete category generated by."  Unlike most other uses
of "complete" in mathematics, completeness of a category is not a property
but a "property-like structure."

Mike

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8 Jul 2009 19:06

### Re: separable locale


Dear Thomas,

as far as I remember, Fourman & Grayson define and study separable locales
toward the end of "Formal spaces".

With best regards

Giovanni Curi

Quoting Thomas Streicher <streicher <at> mathematik.tu-darmstadt.de>:

> Recently rereading Fourman's "Continuous Truth" I came across the term
> "separable locale" but could nowhere find an explanation. Does it mean a
> cHa A for which there exists a countable subset B such that ever a in A is
> the supremum of those b in B with b leq a. This would be the point free
> account of "second countable", i.e. having a countable basis.
> Of course, second countable T_) spaces are separable, i.e. have a
> countable
> dense set.
> Is this reading the "usual" one?
>
> Thomas
>

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10 Jul 2009 00:39

### coherence for lax monoidal cats

Hi,

is there a coherence theorem for lax monoidal cats?

I have

alpha : (A (x) B) (x) C -> A (x) (B (x) C)
rho : A -> A (x) I
lambda : I (x) A -> A

Do I need just the diagrams from MacLanes coherence theorem (suitably
modified)? Or do I need additional ones?

Cheers,
Thorsten

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10 Jul 2009 05:32

### Re: separable locale

"separable" is used also to mean  T_2

Prof. Peter Johnstone wrote:
> Dear Thomas,
>
> I'm pretty sure that what Michael meant by "separable" was what
> most topologists would call "second countable" -- i.e., countably
> generated as a frame. (There are some topology textbooks in which
> this condition is called "completely separable".)
>
> Peter Johnstone
> ---------------------------------
> On Tue, 30 Jun 2009, Thomas Streicher wrote:
>
>> Recently rereading Fourman's "Continuous Truth" I came across the term
>> "separable locale" but could nowhere find an explanation. Does it mean a
>> cHa A for which there exists a countable subset B such that ever a in
>> A is
>> the supremum of those b in B with b leq a. This would be the point free
>> account of "second countable", i.e. having a countable basis.
>> Of course, second countable T_) spaces are separable, i.e. have a
>> countable
>> dense set.
>> Is this reading the "usual" one?
>>
>> Thomas

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`