MMOTO Elements of monoidal topology

Faculty of Science
Autumn 2012
Extent and Intensity
6/0. 1 credit(s). Type of Completion: k (colloquium).
Teacher(s)
Sergejs Solovjovs, Dr., Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Jan Paseka, CSc.
Department of Mathematics and Statistics - Departments - Faculty of Science
Contact Person: Sergejs Solovjovs, Dr., Ph.D.
Supplier department: Department of Mathematics and Statistics - Departments - Faculty of Science
Timetable
Tue 6. 11. 14:00–15:50 M3,01023, Tue 13. 11. 14:00–15:50 M3,01023, Tue 20. 11. 14:00–15:50 M3,01023
Course Enrolment Limitations
The course is offered to students of any study field.
Syllabus
  • 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.

Literature
  • http://www.math.muni.cz/~solovjovs/Lectures.html
Language of instruction
English
Further Comments
The course is taught only once.

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