The term ‘syntax’ refers not to small categories such as algebraic theories or rings, but rather to their PRESENTATION by signatures or by polynomial generators, et cetera. The process of presentation is an adjoint pair quite distinct from the semantical adjoint pair: both
Syntax is NOT the adjoint of semantics.
Syntax is NOT the adjoint of semantics.
Syntax is NOT the adjoint of semantics.
The term ‘syntax’ refers not to small categories such as algebraic theories or rings, but rather to their PRESENTATION by signatures or by polynomial generators, et cetera. The process of presentation is an adjoint pair quite distinct from the semantical adjoint pair: both