Coursera Spring Sale
40% Off Coursera Plus Annual!
Grab it
Explore the mathematical concept of instances of models of double theories in this 59-minute colloquium lecture from the Topos Institute. Delve into the analogy between categories and their sets, extending this relationship to models of arbitrary double theories and their instances. Learn how this framework generalizes categorical database theory beyond the fundamental case of database schemas as small categories, encompassing extensions like attributed C-sets and algebraic profunctors. Discover how structures such as multifunctors from multicategories to Set and models of Lawvere theories fit within this theoretical framework. Examine the category of instances for simple double theories and explore modal double theories as implemented in the CatColab tool for handling categorical structures with multi-ary operations. Understand how standard C-set theory generalizes beyond terminal double theories, including a comprehensive factorization system and Grothendieck construction that establishes equivalences between discrete opfibrations and instance categories.
