  We study the representation theory of the increasing monoid. Our results
provide a fairly comprehensive picture of the representation category: for
example, we describe the Grothendieck group (including the effective cone),
classify injective objects, establish properties of injective and projective
resolutions, construct a derived auto-duality, and so on. Our work is motivated
by numerous connections of this theory to other areas, such as representation
stability, commutative algebra, simplicial theory, and shuffle algebras.

Representation Theory;Commutative Algebra;Combinatorics