TY - JOUR

T1 - On semiflexible, flexible and pie algebras

AU - Bourke, John

AU - Garner, Richard

PY - 2013/2

Y1 - 2013/2

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84866320185&partnerID=8YFLogxK

U2 - 10.1016/j.jpaa.2012.06.002

DO - 10.1016/j.jpaa.2012.06.002

M3 - Article

AN - SCOPUS:84866320185

SN - 0022-4049

VL - 217

SP - 293

EP - 321

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 2

ER -