On semiflexible, flexible and pie algebras

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Authors

BOURKE John Denis GARNER Richard Henry George

Year of publication 2013
Type Article in Periodical
Magazine / Source Journal of Pure and Applied Algebra
MU Faculty or unit

Faculty of Science

Citation
Doi http://dx.doi.org/10.1016/j.jpaa.2012.06.002
Field General mathematics
Keywords 2-category pie limit
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Description We introduce the notion of pie algebra for a 2-monad, these bearing the same relationship to the flexible and semiflexible algebras as pie limits do to flexible and semiflexible ones. We see that in many cases, the pie algebras are precisely those "free at the level of objects" in a suitable sense; so that, for instance, a strict monoidal category is pie just when its underlying monoid of objects is free. Pie algebras are contrasted with flexible and semiflexible algebras via a series of characterisations of each class; particular attention is paid to the case of pie, flexible and semiflexible weights, these being characterised in terms of the behaviour of the corresponding weighted limit functors.
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