A Modern Introduction to Algebraic Goodwillie Calculus
Date
2013-04-25
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Abstract
In this thesis we will investigate the traditional algebraic Goodwillie calculus of Johnson and McCarthy (see [JM03]) from a more modern perspective. In particular, in the recent paper [BJM11], a new perspective on Goodwillie calculus in categories without a basepoint is given using modern machinery such as model categories, and homotopy limits and colimits. This thesis demonstrates that with relatively few modifications this language may be applied in the traditional setting to recover the same constructions found in [JM03]. As a final example, we investigate a result in [KM02] which demonstrates how this language may be applied to recover André-Quillen homology as the first derivative of a particular functor.
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Mathematics
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Jugdev, T. (2013). A Modern Introduction to Algebraic Goodwillie Calculus (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/24796