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Displayed Categories

Benedikt Ahrens ; Peter LeFanu Lumsdaine.

We introduce and develop the notion of *displayed categories*. A displayed category over a category C is equivalent to "a category D and functor F : D --> C", but instead of having a single collection of "objects of D" with a map to the objects of C, the objects are given as a family indexed by&nbsp;[&hellip;]

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Initial Semantics for Reduction Rules

Benedikt Ahrens.

We give an algebraic characterization of the syntax and operational semantics of a class of simply-typed languages, such as the language PCF: we characterize simply-typed syntax with variable binding and equipped with reduction rules via a universal property, namely as the initial object of some&nbsp;[&hellip;]

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Presentable signatures and initial semantics

Benedikt Ahrens ; André Hirschowitz ; Ambroise Lafont ; Marco Maggesi.

We present a device for specifying and reasoning about syntax for datatypes, programming languages, and logic calculi. More precisely, we study a notion of "signature" for specifying syntactic constructions. In the spirit of Initial Semantics, we define the "syntax generated by a signature" to be&nbsp;[&hellip;]

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