Myles Tierney

Myles Tierney

[Joyal, André]

Dear collegues,

A very sad news: my friend and collaborator Myles Tierney passed away this morning
at home in New Jersey after a long illness. His wife Anne Bergeron was with  him.
He had turned 80 years old last month.

I will write later about his contributions to category theory, his fields.

-André

PS: Anne's email address: bergeron.anne@uqam.ca

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Re: Myles Tierney

[Camell Kachour]

Dear André,

This is a very very sad news !

Myles was not only a great mathematician, but also a very human man,
with a very big heart !

All my condolences to his family.

Camell.

On Thu, Oct 5, 2017 at 8:09 PM, Joyal, André <joyal.andre@uqam.ca> wrote:

>
> Dear collegues,
>
> A very sad news: my friend and collaborator Myles Tierney passed away this
> morning
> at home in New Jersey after a long illness. His wife Anne Bergeron was
> with  him.
> He had turned 80 years old last month.
>
> I will write later about his contributions to category theory, his fields.
>
> -André
>
> PS: Anne's email address: bergeron.anne@uqam.ca
>
> [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
>

[For admin and other information see: http://www.mta.ca/~cat-dist/ ]

RE: Myles Tierney

[Joyal, André]

Dear category theorists,

In case you wish to express your condolences to Hanne Tierney,
Myles's first wife, her email address::

  [hannetw@gmail.com]

Hanne and Myles had two children: Myles Junior and Loren.
Myles Junior was killed in 1999 at the age of 34 while covering the civil war as a journalist in Sierra Leones.
Loren was a medical doctor and she died from breast cancer at the age of 42,
leaving three children, James, Cooper and Anna and her husband James M. Mumford.
Myles survived a terrible rock climbing accident in 1980 in the
Shawangunk Mountains in Upstate New York.

Myles and Hanne stayed close until the end, with Hanne
and their grand-children visiting Myles often.

Best,
André


________________________________________
From: Joyal, André [joyal.andre@uqam.ca]
Sent: Thursday, October 05, 2017 2:09 PM
To: categories@mta.ca
Subject: categories: Myles Tierney

Dear collegues,

A very sad news: my friend and collaborator Myles Tierney passed away this morning
at home in New Jersey after a long illness. His wife Anne Bergeron was with   him.
He had turned 80 years old last month.

I will write later about his contributions to category theory, his fields.

-André

PS: Anne's email address: bergeron.anne@uqam.ca


[For admin and other information see: http://www.mta.ca/~cat-dist/ ]

Re: Myles Tierney

[Ross Street]

Dear Andre, Anne and Hanne

The community of category theorists is grieving with you.
We have lost a great member.

Myles was one of the category theorists I met for the first time at John and Eva Gray's home in Urbana in November 1968. Myles is the one who walked most of the way home with me past the U Illinois Math Dept in the cold. I even remember that we talked about relative homological algebra. From the start, I was impressed by his gentle and kind manner. 

Since then we have had many enjoyable times together, in Australia, in Montreal, and at conferences. He remained gentle, kind and positive throughout all the terrible things, explained by Andre and Mike, that he endured.

While on sabbatical at the University of Sydney, Myles and Hanne hosted a dinner featuring a whole lamb cooking on a spit. For a long time Myles had wanted to do that. It turned out to take a bit longer to cook than expected,  even for Myles, who always liked his meat bloody. In the end it was a big success. 

We are thankful to Myles for his immense contribution to mathematics through his individual work, his numerous collaborations, and his inspiring conversations. 

In sympathy,
Ross

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Myles Tierney

[Lawvere, F.]

Dear Friends and Colleagues,

I am deeply sad about the loss of Myles, my friend and a pillar of the
community surrounding Eilenberg and Mac Lane. I highly respected him as a
creative collaborator. Whenever we met at meetings, or spoke on the phone,
even if we had not seen each other for a long time, we knew each others
way of thinking.

Thanks to Andre Joyal for his obituary and the wealth of information
about the work of Myles Tierney. I elaborate below on our collaboration.

Myles and I had independently recognized the need for an axiomatic theory
of sheaves and related matters, and at a gathering in Albrecht Dolds house
near Heidelberg, we agreed to collaborate on the construction of such a
theory during our upcoming stay at Dalhousie University. (Myles had agreed
to join our group of researchers for a year.) Already in the first days of
our seminar Myles made important advances, such as formulating the axioms
of exactness which we knew would have to be theorems of a correct theory
of topos.

He emphasized in general that Grothendieck had made the category (rather
than the space) the central aspect that we should explicitly axiomatize.
We had a pre-publication copy of SGA4 that we consulted frequently. In
that work there was a significant advance over previous formulations of
the sheaf condition: In a pre-sheaf topos, a covering specified by a
Grothendieck topology, was no longer an infinite family of subobjects, but
a single subobject R, (which of course might be imagined to arise as the
union of a family); this made possible the formulation of notions in
finitary terms, indeed in terms of a single operator whose properties
Myles made precise. (Some people object to calling such operators
topologies; the same objection applies to Grothendiecks use of the term
topologies for his equivalent notion, which is of course also not
literally a topology in the classical sense. Later we referred to such an
operator as a localness operator, as a modal operator it is locally the
case that, or as a Tierney closure operator which - as I pointed out to
Kuratowski on his visit to Dalhousie - is not a Kuratowski closure
operator since it preserves intersections, rather than unions. Similar
operators arise in other parts of mathematics where they are sometimes
called 'nuclei'.)

Another unique feature of SGA4 is that it contains no definition of topos;
indeed every rigorous mention is of U-topos. This parameter U was
essentially a model of set theory, and previous work on the category of
sets showed clearly that for mathematical purposes, the use of composition
of mappings is more effective than towers of membership. Thus Myles and I
decided to replace U itself by an arbitrary topos (in our determination of
that term), and indeed a general U-topos E could now be seen as structured
by a morphism E --> U. This provided a suitable codomain for the 2-functor
from internal U-sites to U-toposes, whose image consisted of those E which
contain a bound in U. That, our fundamental preliminary goal, was proved
in his thesis by the remarkable student of Myles, the late Radu
Diaconescu.

We also had available a preliminary version of Monique Hakims thesis
applying Grothendieck's notion of classifier topos to parameterized
complex analysis.  This notion can be seen as a key step of Model Theory,
except that the use of conjunction and disjunction and existential
quantification is replaced by Grothendieck's direct recognition of which
classes of structures are defined in terms of finite limits and small
colimits. Of course, a logician will expect or want primitive predicates
and basic axioms to present such notions of structure, and to facilitate
such recognition. Our initial work to make explicit such a notion of
theory-presentation was carried out by several people. It became evident
that such a construction does not work for general elementary theories,
because the negative operations of universal quantification and
implication are not preserved by the geometrical morphisms of toposes,
even though these operations are well-defined and exist within each
particular topos. (Restricting to open geometric morphisms or to positive
presentations can partly circumvent this limitation.) The positive
presentations need to use the classical idea of sequent, rather than the
mere specification of a class of formulas that aim to be true.

The classifier toposes are useful for mathematical questions other than
logical ones, for example in combinatorial topology, as first pointed out
in detail by Andre Joyal. The relation between combinatorial schemes and
the spaces they generate is an adjoint functor. Specifically, any
structure carried by a unit interval or by other basic space in a topos of
spaces gives rise to the adjoint between the topos of spaces itself and
the classifying topos for such structures, for example, distributive
lattice, Boolean algebra, total ordering. Myles foresaw such clarifying
applications, and in many other ways his knowledge of topology
supplemented my own background.

A useful construction made explicit by Myles is still not widely
recognized: the category of co-algebras for a given left-exact comonad in
a given topos, is indeed another topos. This can be seen as an essential
step in the construction of a pre-sheaf topos.

A significant advance in the world of logic was the result of Diaconescu,
showing that the axiom of choice implies Boolean logic. His professor
Myles Tierney had proved the independence of the continuum hypothesis,
making essential use of the notion of sheaf. (LNM 274*). It was in
preparing his talks for our seminar 1969-1970 that Myles formulated most
of the logic needed for that result. Sabah Fakir who took part in these
seminars sent notes each week to Jean Benabou who also gave a seminar
simultaneously. Anders Kock was a very active participant, whose later
Aarhus seminar with Gavin Wraith also contributed to the rapid
dissemination of the results and the general point of view.

After I had presented our results at the 1970 ICM, we organized an
international meeting in January 1971; Myles returned from Rutgers to
Halifax to explain the continuum hypothesis to the 70 participants.

Myles and I were gratified in the ensuing months and years to see that our
general point of view was taken up by many mathematicians and logicians.
Further applications, for example the role of Boolean sheaves in algebraic
geometry, still await detailed publication. Several works by Michael Barr
intiated such applications.

In 1974 Myles Tierney and Alex Heller organized a meeting in New York City
in honor of Samuel Eilenbergs 60th birthday; they edited the proceedings
as Algebra, Topology, and Category Theory**. That book contains an
influential article by Myles on the construction of classifier toposes for
internal sites. Myles Tierney, Fred Linton, Jon Beck and I were roughly
the same age when we started our studies at Columbia University; Mike
Barr, Peter Freyd, John Gray, and Barry Mitchell were senior to us, and
collaborated with us too. Sammy had attracted a group, all of whom
continued to contribute to category theory.

In the ensuing years Myles organized a regular seminar in New York on
weekends. It was attended by categorists from several states. I attended
the seminar frequently from Buffalo, and I took along several students
including Kimmo Rosenthal and Phil Mulry. Thanks to the generosity of
Myles and Hanne, everybody was invited to sleep on the floor of their
loft.

When I last spoke with Myles on the phone just a few months ago he
explained to me the specific topological intuition underlying the notion
of Kan complex.

I know that Myles would have joined me in welcoming any future mathematics
on the horizon for which our work might have provided a stepping stone.

Bill Lawvere

  * Toposes, Algebraic Geometry and Logic. LNM 274, Springer 1972

** Algebra, Topology, and Category Theory, Academic Press, 1976



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Re: Myles Tierney

[Marta Bunge]

Dear Anne, 

I join you in your grief to have lost one of the most prominent members of our group and someone whom I have known since the early days when I presented my thesis at an Oberwolfach meeting in 1966 then meeting the entire Sammy-gang. My condolences extend to Hanne and their grandchildren. I knew from  her how brave Myles has been in face of his devastating illness. He has my  profound admiration as do you. He will never be forgotten. Only today I was communicating to others my very old paper on topos theory and the independence of Souslin hypothesis which was greatly influenced by Myles having dealt beautifully with the topos proof for the independence of of CH after Paul Cohen, just as mine was influenced by one by Stanley Tennembaum. This was not the only influence that Myles has had on me. His forcing topologies led to my construction of the symmetric topos of  the Lawvere distributions classifier and of course much much more. I will miss him. This is a very bad year for us category theorists. 

Best wishes 
Marta

----- Original Message -----
From: "Joyal, André" <joyal.andre@uqam.ca>
To: categories@mta.ca
Sent: Thursday, October 5, 2017 2:09:26 PM
Subject: categories: Myles Tierney

Dear collegues,

A very sad news: my friend and collaborator Myles Tierney passed away this morning
at home in New Jersey after a long illness. His wife Anne Bergeron was with   him.
He had turned 80 years old last month.

I will write later about his contributions to category theory, his fields.

-André

PS: Anne's email address: bergeron.anne@uqam.ca


[For admin and other information see: http://www.mta.ca/~cat-dist/ ]