… HIGHER CATEGORIES AND HOMOTOPICAL ALGEBRA … through the lens of higher
categories after Joyal and Lurie, … of research in algebraic topology and algebraic geometry in the …

… the algebraic structure of a simple type theory, which are described precisely by a class of
arities, induce polynomial functors in presheaf categories whose algebras are exactly models …

… 1)-category is presented by some model category to … higher inductive type; thus we might
say that higher inductive types replace the large unwieldy cell complexes of classical algebraic …

… Furthermore, as we explain below, they have influenced subsequent work in several algebraic
… is Cohn [32]; this book also discusses some category theory and some applications to …

… Taking inspiration from the (trivial) fibrations in a cofibrantly generated model category we
observe that they can be made algebraic because they can be captured using lifting properties…

… Our goal is to show that under mild hypotheses, the two versions of “algebra” give equivalent
2-category. The mismatch is visible already in two (spacetime) dimensions. (Although our …

… that local fusion higher categories classify the anomaly-free algebraic higher symmetries,
while anomalous algebraic higher symmetries are described by generic higher categories. In …

… categories of such models. We show that no such composite has the exceptional Jordan
algebra as … with a preferred embedding in a complex matrix algebra. We show that these can be …

… To define functorial cylinder objets in the category of dg P ¡ -coalgebras, we consider two
algebraic models for the interval, the first one in the category of dg coassociative coalgebras …

… consider a category whose objects are algebras, we assume that the morphisms are the
algebraic … The following summarizes some useful algebraic properties of objects of previously-…