4 Dec
1992
4 Dec
'92
3 a.m.
what in the world is the Beck-Chevalley condition?
Bill Lawvere ("Adjointness in Foundations", Dialectica, 23 (1969) 281-296) observed that the quantifiers are the adjoints to substitution However mere category theory is not sufficient to capture exactly the syntactic properties of quantification. The Beck-Chevalley condition says that you can substitute inside quantifiers. where the categorical formulation is as Ross Street gave it. Jean B\'enabou, Robert Seely and others have studied aspects of it in detail. Paul ==============================================================================