4 papers
From Semantics to Syntax: A Type Theory for Comprehension Categories
Niyousha Najmaei, Niels van der Weide, Benedikt Ahrens +1
Recent models of intensional type theory have been constructed in algebraic weak factorization systems (AWFSs). AWFSs give rise to comprehension categories that feature non-trivial…
Comparing semantic frameworks for dependently-sorted algebraic theories
Benedikt Ahrens, Peter LeFanu Lumsdaine, Paige Randall North
Algebraic theories with dependency between sorts form the structural core of Martin-Löf type theory and similar systems. Their denotational semantics are typically studied using ca…
Insights From Univalent Foundations: A Case Study Using Double Categories
Nima Rasekh, Niels van der Weide, Benedikt Ahrens +1
Category theory unifies mathematical concepts, aiding comparisons across structures by incorporating objects and morphisms, which capture their interactions. It has influenced area…
Univalent Double Categories
Niels van der Weide, Nima Rasekh, Benedikt Ahrens +1
Category theory is a branch of mathematics that provides a formal framework for understanding the relationship between mathematical structures. To this end, a category not only inc…