Codescent objects and coherence

Stephen Lack

This appeared in Journal of Pure and Applied Algebra 175:223-241, 2002.

We introduce 2-categorical colimit notions called codescent objects of coherence data, and lax codescent objects of lax coherence data, and use them to study the inclusion, T-Algs-->Ps-T-Alg, of the 2-category of strict T-algebras and strict T-morphisms of a 2-monad T into the 2-category of pseudo T-algebras and pseudo T-morphisms; and similarly the inclusion T-Algs-->Lax-T-Algl, where Lax-T-Algl has lax algebras and lax morphisms rather than pseudo ones. We give sufficient conditions under which these inclusions have left adjoints. We give sufficient conditions under which the first inclusion has left adjoint for which the components of the unit are equivalences, so that every pseudo algebra is equivalent to a strict one.

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Steve Lack
Last modified: Fri Aug 30 09:11:18 EST 2002