Logic from the Point of View of Category Theory 2007/8
A semestral course at the
Department of Logic,
Faculty of Philosophy and Arts,
Charles University in Prague,
in the summer term 2007/8
(faculty code ALGV00008);
a follow-up of the course
Category Theory from the Point of View of Logic.
A similar course was run in 2009/10.
(RTF, in Czech)
Summary of lectures
- 26 Feb 2008: Elements and properties (Lawvere-Rosebrugh: Sets for Mathematics, ch. 1)
- Constant and variable elements, bivalent and many-valued properties, separator and co-separator.
- 4 Mar 2008: Exponentiation (Goldblatt: Topoi, s. 3.16)
- Exponentiation, Cartesian closed categories.
- 11 Mar 2008: Subobject classification (Goldblatt: Topoi, s. 4.1-2)
Subobjects, subobject classifier, elementary topos.
- 18 Mar 2008: Examples of topoi (Goldblatt: Topoi, s. 4.3-5)
Counterexamples on subobject classifiers and co-separators (by Jan Saroch), constructions of categories, examples of topoi, bundles (Mar 25).
- 25 Mar 2008: Truth functions in topoi (Goldblatt: Topoi, s. 6.6-7)
Truth functions in topoi, algebra of subobjects (Apr 1).
- 1 Apr 2008: Topos logic (Goldblatt: Topoi, s. 7.1-2)
Boolean topoi, valuation and validity in topoi.
- 15 Apr 2008: Choice and natural numbers (Goldblatt: Topoi, s. 12.1-2)
Axiom of choice (Apr 1), natural number object.
- 23 Apr 2008: An elementary theory of the category of sets
Lawvere's 1964 paper on ETCS (student talks).
- 29 Apr 2008: Functors and natural transformations (Goldblatt: Topoi, s. 9.1-2)
Covariant and contravariant functors (Apr 15). Natural transformations, equivalence of categories (a student talk).
- 6 May 2008: Categories in logic and computer science, CCAF
Goguen's Categorical Manifesto (29 Apr, 6 May, student talks), categories of signatures and algebras (student talks), McLarty's axiomatization CC of the category of categories (a student talk).