6533b82ffe1ef96bd1295268

RESEARCH PRODUCT

Double adjunctions and free monads

N GambinoTm FioreJ Kock

subject

Double category adjunction monad18D05 (Primary) 18C15 18C20 (Secondary)Mathematics::Category TheoryFOS: MathematicsCategory Theory (math.CT)Mathematics - Category TheoryMathematics::Algebraic Topology

description

We characterize double adjunctions in terms of presheaves and universal squares, and then apply these characterizations to free monads and Eilenberg--Moore objects in double categories. We improve upon our earlier result in "Monads in Double Categories", JPAA 215:6, pages 1174-1197, 2011, to conclude: if a double category with cofolding admits the construction of free monads in its horizontal 2-category, then it also admits the construction of free monads as a double category. We also prove that a double category admits Eilenberg--Moore objects if and only if a certain parameterized presheaf is representable. Along the way, we develop parameterized presheaves on double categories and prove a double-categorical Yoneda Lemma.

yearjournalcountryeditionlanguage
2011-05-31
https://hdl.handle.net/21.11116/0000-0004-1FC2-F21.11116/0000-0004-1FC0-1