Chad Mitchell Nester, the PhD student of the Department of Software Science, will defend his PhD thesis "Partial and Relational Algebraic Theories" on February 1, 2024, starting at 14:00. The defense will take place in room ICT-638 (Akadeemia tee 15a, ICT building of TalTech) and can be also followed via Zoom.
This thesis introduces notions of partial algebraic theory and relational algebraic theory, in which operations are interpreted as partial functions and as relations, respectively. The development focuses on the monoidal category structure of partial functions and relations. In particular, partial and relational algebraic theories are both intuitively presentable by means of string diagrams for monoidal categories, which play the role of terms. The varieties — those categories that arise as the category of models of a given theory — are rigorously characterised for both partial algebraic theories and relational algebraic theories. Specifically, the varieties associated with partial algebraic theories are precisely the locally finitely presentable categories, while the varieties associated with relational algebraic theories are precisely the definable categories
The thesis is published in the Digital Collection of TalTech Library.
Supervisor: prof Pawel Maria Sobocinski.
Oponents:
- Prof. Paul Levy, University of Birmingham, United Kingdom;
- Prof. Marino Miculan, University of Udine, Italy.
Meeting ID: 950 0313 1541
Passcode: 160532