Book available

Book available

[tholen]

Dear ?categories? readers,

This is to draw your attention to the recently published book

?MONOIDAL TOPOLOGY --  A Categorical Approach to Order, Metric , and
Topology?,

edited by Dirk Hofmann, Gavin J. Seal and Walter Tholen. It appeared in
the ?Encyclopedia of Mathematics and Its Applications? series of
Cambridge University Press, as vol. 153; see

www.cambridge.org/9781107063945


This 500-page book gives a rather self-contained introduction to the
subjects mentioned in its title, including category theory itself. The
list of contents below (including chapter authors and lengths of
chapters) may describe best to you what to expect. Largely absent is a
treatment of (Cauchy-Lawvere-type) completeness which, together with
other more advanced themes, is to be treated in a follow-up book.

Regards,
Walter


I      Introduction (Robert Lowen, Walter Tholen; 14pp)
    1   The ubiquity of monoids and their actions
    2   Spaces as categories, and categories of spaces
    3   Chapter highlights and dependencies

II     Monoidal structures (Gavin J. Seal, Walter Tholen; 127pp)
1	Ordered sets
2	Categories and adjunctions
3	Monads
4	Monoidal and ordered categories
5	Factorizations, fibrations, and  topological functors

III   Lax algebras (Dirk Hofmann, Gavin J. Seal, Walter Tholen; 139pp)
1	Basic concepts
2	Fundamental examples
3	Categories of lax algebras
4	Embedding lax algebras into a quasitopos
5	Representable lax algebras

IV   Kleisli monoids (Dirk Hofmann, Robert Lowen, Rory Lucyshyn-Wright,
Gavin J. Seal; 91pp)
1	Kleisli monoids and lax algebras
2	Lax extensions of monads
3	Lax algebras as Kleisli monoids
4	Injective lax algebras as Eilenberg-Moore algebras
5	Domains as lax algebras and Kleisli monoids

V   Lax algebras as spaces (Maria Manuel Clementino, Eva Colebunders,
Walter Tholen; 92pp)
1	Hausdorff separation and compactness
2	Low separation, regularity, and normality
3	Proper and open maps
4	Topologies on a category
5	Connectedness





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