2021/03/02 by John L. MacDonald, MacDonald, John Lauchlin, Laura Scull +1
Mathematics · Medicine · #18N15 #18N50 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Intracranial Aneurysms: Treatment and Complications
paper · pdf · doi:10.48550/arxiv.2103.02001
openalex publication_date 2021/03/02 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
We use the general notion of 2-dimensional adjunction with given coherence\nequations as introduced by MacDonald-Stone, building on earlier work by Gray,\nto derive coherence equations for a general 2-monad, which we refer to as a\nlax-Gray monad. The free lax-Gray 2-monad on one object may be regarded as the\nsuspension of a lax 2-dimensional analogue of the simplicial category Delta. We\ncall this analogue Delta LG for lax-Gray Delta. This is analogous to the way\nthat the free 1-monad Mnd (as presented in Schanuel-Street) is a concrete\nexample of the suspension of the simplicial category Delta, described by Mac\nLane.\n