Details

Autor(en) / Beteiligte

• Freyd, P. J
• Scedrov, A

Titel

Chapter Two Allegories

Ist Teil von

• Categories, Allegories, 1990, Vol.39, p.195-263

Ort / Verlag

The Netherlands: Elsevier Science & Technology

Erscheinungsjahr

1990

Quelle

ScienceDirect eBooks

Beschreibungen/Notizen

• This chapter discusses the distributive, power, and quotient allegories. Allegories are to binary relations between sets as categories are to functions between sets. A (unitary) representation of allegories is a functor between allegories which preserves (units,) reciprocation and intersection. As a functor, it preserves the category structure, and thus, in particular, composition. The definitions of map and tabulation are equational, hence maps and tabulations are preserved by representations of allegories. Allegories with finite unions are considered that distribute with composition, but not necessarily with intersection. A pre-power allegory is defined as a division allegory in which each object appears as the target of a thick morphism. The quotient allegory is the allegory of equivalence classes with the obvious operations that makes the assignment of equivalence classes into a representation of allegories. The chapter focuses on amenable congruences—that is, congruences that respect binary unions and such that congruence class R has the largest element.