Gould, Miles Richard
(2008)
Coherence for categorified operadic theories.
PhD thesis, University of Glasgow.
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Abstract
Given an algebraic theory which can be described by a (possibly symmetric) operad P, we propose a definition of the weakening (or categorification) of the theory, in which
equations that hold strictly for P algebras hold only up to coherent isomorphism. This generalizes the theories of monoidal categories and symmetric monoidal categories, and
several related notions defined in the literature. Using this definition, we generalize the result that every monoidal category is monoidally equivalent to a strict monoidal category, and show that the “strictification” functor has an interesting universal property, being left
adjoint to the forgetful functor from the category of strict P categories to the category of weak P categories. We further show that the categorification obtained is independent of our choice of presentation for P , and extend some of our results to manysorted theories,
using multicategories.
Item Type: 
Thesis
(PhD)

Qualification Level: 
Doctoral 
Keywords: 
category theory, universal algebra, categorification, higherdimensional algebra, monoidal categories, operads, linear theories, strongly regular theories, strictification, coherence 
Subjects: 
Q Science > QA Mathematics 
Colleges/Schools: 
College of Science and Engineering > School of Mathematics and Statistics > Mathematics 
Supervisor's Name: 
Leinster, Dr. Tom 
Date of Award: 
2008 
Depositing User: 
Mr Miles Gould

Unique ID: 
glathesis:2008689 
Copyright: 
Copyright of this thesis is held by the author. 
Date Deposited: 
14 Apr 2009 
Last Modified: 
10 Dec 2012 13:24 
URI: 
http://theses.gla.ac.uk/id/eprint/689 
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