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Thomas, O'Neill.
Differential Forms for T-Algebras in *Kahler* Categories
.

Degree: 2013, University of Ottawa

URL: http://hdl.handle.net/10393/24217

A Kahler category axiomatizes the algebraic geometric theory of Kahler Differentials in an abstract categorical setting. To facilitate this, a Kahler category is equipped with an algebra modality, which endows each object in the image of a specified monad with an associative algebra structure; universal derivations are then required to exist naturally for each of these objects. Moreover, it can be demonstrated that for each T-algebra of said monad there is a natural associative algebra structure.
In this paper I will show that under certain conditions on the Kahler category, the universal derivations for the algebras arising from T-algebras exist and arise via a coequalizer. Furthermore, this result is extended to provide an alternative construction for universal derivations for a more general class of algebras, including all algebras in a Kahler category. A prospective categorical formulation of the theory of noncommutative Kahler differentials is then given, and the above said results are shown to apply in this context. Finally, another class of algebras is constructed via a colimit, and the modules of differential forms for these algebras is computed.

Subjects/Keywords: Category Theory; Kahler Differentials; Abstract Differentiation; T-Algebras

…between the
classical theory of K¨
ahler *differentials* and K¨
ahler categories that whereas… …categories due to Cockett, which categorifies the notion of noncommutative K¨
ahler *differentials*… …*differentials* allows one to formulate de Rham cohomology algebraically, and hence noncommutative K… …ahler *differentials* ostensibly offer a
means for developing de Rham cohomology for… …theory of noncommutative K¨
ahler *differentials* is abstracted in such a way that makes…

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APA (6^{th} Edition):

Thomas, O. (2013). Differential Forms for T-Algebras in Kahler Categories . (Thesis). University of Ottawa. Retrieved from http://hdl.handle.net/10393/24217

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Thomas, O'Neill. “Differential Forms for T-Algebras in Kahler Categories .” 2013. Thesis, University of Ottawa. Accessed August 21, 2019. http://hdl.handle.net/10393/24217.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Thomas, O'Neill. “Differential Forms for T-Algebras in Kahler Categories .” 2013. Web. 21 Aug 2019.

Vancouver:

Thomas O. Differential Forms for T-Algebras in Kahler Categories . [Internet] [Thesis]. University of Ottawa; 2013. [cited 2019 Aug 21]. Available from: http://hdl.handle.net/10393/24217.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Thomas O. Differential Forms for T-Algebras in Kahler Categories . [Thesis]. University of Ottawa; 2013. Available from: http://hdl.handle.net/10393/24217

Not specified: Masters Thesis or Doctoral Dissertation