papers available

papers available

[tholen]

I have made the following recent papers available from my home page at

www.math.yorku.ca/~tholen

I appreciate receiving any comments that you may have.

Regards,
Walter.

-------------------------------------

Marco Grandis and Walter Tholen: Natural weak factorization systems

Abstract. In order to facilitate a natural choice for morphisms created
by the (left or right) lifting property as used in the definition of
weak factorization systems, the notion of natural weak factorization
system in the category K is introduced, as a pair (comonad, monad) over
K^2. The link with existing notions in terms of morphism classes is
given via the respective Eilenberg-Moore categories.

-------------------------------------

Jiri Rosicky and Walter Tholen: Factorization, fibration and torsion

Abstract.  A simple definition of torsion theory is presented, as a
factorization system with both classes satisfying the 3-for-2 property.
Comparisons with the traditional notion are given, as well as
connections with the notions of fibration and of weak factorization
system, as used in abstract homotopy theory.

-------------------------------------

Eraldo Giuli and Walter Tholen: A topologist's view of Chu spaces

Abstract. For a symmetric monoidal-closed category X and any object K,
the category of K-Chu spaces is small-topological over X and
small-cotopological over X^op. It's full subcategory of M-extensive
K-Chu spaces is topological over X when X is M-complete, for any
morphism class M. Often they form a full coreflective subcategory of
Diers' category of affine K-spaces. Hence, in addition to their roots
in in the theory of pairs of topological vector spaces (Barr) and in
the study of event structures for modeling concurrent processes
(Pratt), Chu spaces seem to have a less explored link with algebraic
geometry. We use the Zariski closure operator to characterize the
self-dual category of M-extensive and M-coextensive K-Chu spaces.

Papers available

[Thorsten Palm]

Dear categorists,

My Ph.D. dissertation, entitled `Dendrotopic Sets for Weak
Infinity-Categories', and a preliminary version of my paper
`Dendrotopic Sets' can now be downloaded from the web-page

   www.math.yorku.ca/Who/Grads/palm .

The content of the two works is summarized below, where they are
referred to as [A] and [B] respectively.

Best regards

Thorsten Palm


----------------

In his unpublished paper [1], Makkai defined a notion of _weak
infinity-category_ (under the name `multitopic omega-category'). The
underlying geometric structures, called _multitopic sets_, are
described in the three-part paper [2]. Makkai takes a weak
infinity-category to be a multitopic set with the mere property that
_compositions_ exist, which are defined as equivalences of certain
_coslice_ objects.

[A] gives a definition of weak infinity-categories equivalent to
Makkai's. While this definition falls into the same two stages, it is
considerably shorter and more elementary in each of them. The
description of the underlying geometric structures, called
_dendrotopic sets_ here, is done purely combinatorially (whereas [2]
uses the algebraic machinery of multicategories). A coslice object
comes in two guises, in both of which it is a dendrotopic set with
mild extra structure in the form of a dendrotopic map (whereas in [1]
it is a model for a new signature for Makkai's first-order logic with
dependent sorts).

[A] also presents an alternative method of introducing composition to
a dendrotopic set. Here one has to impose the extra structure of a
_universality system_: a subset that behaves in such a way that each
member can be thought of as a universal arrow. The main theorem of [A]
states that a dendrotopic set containing a universality system is a
Makkai weak infinity-category.

The concept of a dendrotopic set is defined at a more leisurely
pace in [B], where the equivalence to the concept of a multitopic
set is, indirectly, established.

References:

[1] M. Makkai: `The multitopic omega-category of all multitopic
omega-categories'; mystic.biomed.mcgill.ca/Makkai

[2] C. Hermida, M. Makkai, A. J. Power: `On weak higher dimensional
categories'; Journal of Pure and Applied Algebra. Part 1: 154 (2000),
pp. 221-246; part 2: 157 (2001), pp. 247-277; part 3: 166 (2002), pp.
83-104

papers available

[Walter Tholen]

This is just to let you know that now ps-files of the following papers
(written during the past few months) are available via my home page at
http://www.math.yorku.ca/Who/Faculty/Tholen/research.html
Alternatively, I am happy to send hard copies upon request.

Regards, Walter.



J. Adamek, H. Herrlich, J. Rosicky, W. Tholen:
"On a generalized Small-Object Argument for the Injective Subcategory Problem"

J. Adamek, H. Herrlich, J. Rosicky, W. Tholen:
"Weak factorization systems and topological functors"

W. Tholen:
"Essential weak factorization systems"

M.M. Clementino, D. Hofmann, W. Tholen:
"The convergence approach to exponentiable maps"

G. Richter, W. Tholen:
"Perfect maps are exponentiable - categorically"