#
Lifting PIE limits with strict projections

##
Martin Szyld

We give a unified direct proof of the lifting of PIE limits to the
2-category of algebras and (pseudo) morphisms, which specifies
precisely which of the projections of the lifted limit are strict and
detect strictness. In the literature, these limits were lifted one by
one, so as to keep track of these projections in each case. We work in
the more general context of weak algebra morphisms, so as to include
lax morphisms as well. PIE limits are also all simultaneously lifted
in this case, provided some specified arrows of the diagram are pseudo
morphisms. Again, this unifies the previously known lifting of many
particular PIE limits, which were also treated separately.

Keywords:
PIE limit, 2-monad, 2-algebra, 2-category

2010 MSC:
Primary: 18D05. Secondary: 18A30

*Theory and Applications of Categories,*
Vol. 34, 2019,
No. 1, pp 1-12.

Published 2019-01-14.

http://www.tac.mta.ca/tac/volumes/34/1/34-01.pdf

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