* a paper available
@ 2009-12-29 15:52 Marek Zawadowski
0 siblings, 0 replies; only message in thread
From: Marek Zawadowski @ 2009-12-29 15:52 UTC (permalink / raw)
To: categories
The following paper
Lax Monoidal Fibrations
Abstract: We introduce the notion of a lax monoidal fibration
and we show how it can be conveniently used to deal with various
algebraic structures that play an important role in some definitions
of the opetopic sets (Baez-Dolan, Hermida-Makkai-Power). We present
the 'standard' such structures, the exponential fibrations of basic
fibrations and three areas of applications. First area is related
to the T-categories of A. Burroni. The monoids in the Burroni lax
monoidal fibrations form the fibration of T-categories.
The construction of the relative Burroni fibrations and free
T-categories in this context, allow us to extend the definition
of the set of opetopes given by T. Leinster to the category
of opetopic sets (internally to any Grothendieck topos, if needed).
We also show that fibration of (1-level) multicategories, considered
by Hermida-Makkai-Power, is equivalent to the fibration of
(finitary, cartesian) polynomial monads. This equivalence is induced
by the equivalence of lax monoidal fibrations of amalgamated signatures,
polynomial diagrams, and polynomial (finitary, endo) functors. Finally,
we develop a similar theory for symmetric signatures, analytic diagrams
(a notion introduced here), and (finitary, multivariable) analytic
(endo)functors. Among other things we show that the fibrations of
symmetric multicategories is equivalent to the fibration of analytic
monads. We also give a characterization of such a fibration of analytic
monads. An object of this fibration is a weakly cartesian monad on
a slice of Set whose functor parts is a finitary functors weakly
preserving wide pullbacks. A morphism of this fibration is a weakly
cartesian morphism of monads whose functor part is a pullback functor.
is available at
http://arxiv.org/abs/0912.4464
and at my home-page
http://www.mimuw.edu.pl/~zawado/papers.htm
Comments are welcome.
Happy New Year to all,
Marek Zawadowski
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
^ permalink raw reply [flat|nested] only message in thread
only message in thread, other threads:[~2009-12-29 15:52 UTC | newest]
Thread overview: (only message) (download: mbox.gz / follow: Atom feed)
-- links below jump to the message on this page --
2009-12-29 15:52 a paper available Marek Zawadowski
This is a public inbox, see mirroring instructions
for how to clone and mirror all data and code used for this inbox;
as well as URLs for NNTP newsgroup(s).