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Characterising E-projectives via Comonads

Published online by Cambridge University Press:  12 May 2015

WENG KIN HO
WENG KIN HO*
Affiliation:
Mathematics and Mathematics Education, National Institute of Education, Nanyang Technological University, 637616 Singapore Email: wengkin.ho@nie.edu.sg
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Abstract

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This paper demonstrates the usefulness of a comonadic approach to give previously unknown characterisation of projective objects in certain categories over particular subclasses of epimorphisms. This approach is a simple adaptation of a powerful technique due to Escardó which has been used extensively to characterise injective spaces and locales over various kinds of embeddings, but never previously for projective structures. Using some examples, we advertise the versatility of this approach – in particular, highlighting its advantage over existing methods on characterisation of projectives, which is that the comonadic machinery forces upon us the structural properties of projectives without relying on extraneous characterisations of the underlying object of the coalgebra arising from the comonad.

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Type
Paper
Information
Mathematical Structures in Computer Science , Volume 27 , Special Issue 4: Symposium on Domain Theory (ISDT 2013) , May 2017 , pp. 491 - 506
Copyright
Copyright © Cambridge University Press 2015 

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