定義 (quiver)
とを共にclassとする。
また、に対し、
定義から明らかに、
が成り立つ。
定義 (deductive system)
が文脈から明らかな時、をのように省略して書く。
の時、定義から
だが、これは1-point ruleによって
と同値。
定義 (category)
定義 (small category, locally small category)
参考文献
- M. Arbib and E. Manes. Arrows, Structures and Functors — The Categorical Imperative. Academic Press, 1975.
- S. Awodey. Category Theory. 2d ed. Oxford University Press, 2010.
- M. Barr and C. Wells. Category Theory for Computing Science. Prentice Hall, 1990.
- R.C. Backhouse. Mathematics of Program Construction. Unpublished.
- R. Bird and O. de Moor. Algebra of Programming. Series in Computer Science. Prentice-Hall, 1997.
- D. Gries. Foundations for Calculational Logic. In M. Broy, B. Schieder, eds., Mathematical Methods in Program Development. Springer, 1997.
- E.J. Lemmon. Introduction to Axiomatic Set Theory. Routledge & Kegan Paul, 1968.
- D. Gries and F.B. Schneider. A Logical Approach to Discrete Math. Springer-Verlag, 1993.
- S. Mac Lane. Categories for the Working Mathematician. 2d ed. Springer-Verlag, 1998.
- G. Tourlakis. Lectures in Logic and Set Theory Vol. 1: Mathematical Logic. Cambridge University Press, 2003.
- G. Tourlakis. Lectures in Logic and Set Theory Vol. 2: Set Theory. Cambridge University Press, 2003.
- G. Tourlakis. Mathematical Logic. John Wiley & Sons, 2008.