Please note: You are viewing the unstyled version of this web site. Either your browser does not support CSS (cascading style sheets) or it has been disabled.

Macquarie University  Department of Mathematics

Local Navigation

Workshop on Categorical Methods in Algebra, Geometry and Mathematical Physics

Satellite to the StreetFest conference in honour of Ross Street's sixtieth birthday

July 18-21 2005, Australian National University, Canberra

Tue, 19 July:  17:00 - 17:40

On Lawvere-completeness for lax algebras
Clementino, Maria Manuel (Universidade de Coimbra)

The notion of reflexive and transitive $(T,V)$-algebra --- or $(T,V)$-category ---, for a symmetric monoidal-closed category $V$ and a lax monad $T$ in the category of $V$-matrices, has been recently introduced and studied \bibref{2,3}. It comprises $V$-categories, when $T$ is the identity monad, and Barr's relational algebras \bibref{1}, when $V=2$. Although it was this latter instance that raised the subject --- having in mind that several interesting results of convergence structures could be generalized to other settings --- the former one gives a new insight to these structures. Indeed, a considerable amount of knowledge of $V$-categories can be interpreted in the general setting of $(T,V)$-categories.

In this talk we will concentrate on Lawvere's notion of (Cauchy-)complete $V$-category. We will deal with a (possible) generalization of this concept, explore some examples and results.

\begin{references}
\bibitem M.\ Barr, {\em Relational algebras}, in: Springer Lecture Notes in Math.\ 137 (1970), 39--55.
\bibitem M.M.\ Clementino and D.\ Hofmann, {\em Topological features of lax algebras}, Appl.\ Categ.\ Struct.\ 11 (2003), 267--286.
\bibitem M.M.\ Clementino and W.\ Tholen, {\em Metric, Topology and Multicategory -- a Common Approach}, J.\ Pure Appl.\ Algebra 179 (2003), 13--47.
\bibitem F.W.\ Lawvere, {\em Metric spaces, generalized logic, and closed categories}, Rend.\ Sem.\ Mat.\ Fis.\ Milano 43 (1973), 135--166.
\end{references}

Typeset PDF of this abstract.