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.

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).