PřF:MMOTO Elements of monoidal topology

MMOTO Elements of monoidal topology

Přírodovědecká fakulta
podzim 2012

Rozsah

6/0. 1 kr. Ukončení: k.

Vyučující

Sergejs Solovjovs, Dr., Ph.D. (přednášející)

Garance

Rozvrh

Út 6. 11. 14:00–15:50 M3,01023, Út 13. 11. 14:00–15:50 M3,01023, Út 20. 11. 14:00–15:50 M3,01023

Omezení zápisu do předmětu

Předmět je otevřen studentům libovolného oboru.

Osnova

Monoidal topology is an approach to categorical topology based in monads and quantales. Motivated by the representation of topological spaces as lax relational algebras for the ultrafilter monad on the category of sets, it replaces the ultrafilter monad with an arbitrary monad T, and the two-element chain with a unital quantale V, thereby getting the construct (T,V)-Cat of (T,V)- categories and (T,V)-functors. Examples of these constructs include the categories of topological space, preordered sets, (probabilistic) metric spaces, closure spaces, and approach spaces. The constructs (T,V)-Cat also have convenient properties, e.g., are topological.
The lectures will introduce the constructs (T,V)-Cat in full detail; show how to incorporate the above-mentioned examples in their framework; describe their basic properties; and consider an example of the application of their theory to general topology, i.e., a generalization of the Kuratowski- Mrowka theorem on the equivalence between the concepts of proper and perfect map.

Literatura

Vyučovací jazyk

Angličtina

Další komentáře

Předmět je vyučován jednorázově.