Two-dimensional monad theory
This is the first in a series of articles (to include and extend unpublished PhD thesis material of Kelly's students R. Blackwell and G. Bird) on the universal algebra of categories with structure. The centre- piece is the 2-category T-Alg of algebras for a ranked monad T on a suitable 2-category. Here the algebras are strict, while the morphisms merely preserve the action up to a given coherent isomorphism. Certain 2-categorical limits and colimits are shown to exist in T-Alg. These suffice to imply (with the assistance of ``flexible'' algebras) the cocompleteness of T-Alg as a bicategory. Every ``algebraic'' 2-functor T- Alg\(\to S\)-Alg is proved to admit a left adjoint in the bicategorical sense.
universal algebra of categories with structure
scientific article; zbMATH DE number 4105188
scientific article