Mahavier completeness and classifying diagrams

Yuki Maehara, Ittay Weiss*

*Corresponding author for this work

    Research output: Contribution to journalArticle

    1 Citation (Scopus)

    Abstract

    Generalised inverse limits of compacta were introduced by Ingram and Mahavier in 2006. The main difference between ordinary inverse limits and their generalised cousins is that the former concerns diagrams of singlevalued functions while the latter permits multivalued functions. However, generalised inverse limits are not merely limits in the Kleisli category of a hyperspace monad, a fact that independently motivated each of the authors of this article to come up with the same formalism which restores the link with category theory through the concept of Mahavier limit of an order diagram in an order extension of a category B. Mahavier limits of diagrams in B coincide with ordinary limits in B, and so Mahavier limits are an extension of ordinary limits along the functor that views an ordinary diagram as a diagram in the extension. Within that context it is natural to consider Mahavier completeness, namely when all small diagrams admit Mahavier limits, as well as classifying diagrams, namely the existence of a right adjoint to the mentioned functor on diagrams. In this work we show that these two conditions are equivalent, and we study some of the properties of classifying diagrams and of the adjunction.

    Original languageEnglish
    Pages (from-to)55-69
    Number of pages15
    JournalTopology and its Applications
    Volume229
    DOIs
    Publication statusPublished - 15 Sep 2017

    Keywords

    • category with order
    • classifying diagram
    • generalised categorical limit
    • generalised inverse limit
    • generalised inverse system
    • inverse system
    • mahavier limit
    • multivalued function
    • upper semicontinuous function

    Fingerprint Dive into the research topics of 'Mahavier completeness and classifying diagrams'. Together they form a unique fingerprint.

    Cite this