The weak theory of monads |
| |
Authors: | Gabriella Böhm |
| |
Institution: | Research Institute for Particle and Nuclear Physics, Budapest, H-1525 Budapest 114, PO Box 49, Hungary |
| |
Abstract: | We construct a ‘weak’ version EMw(K) of Lack and Street's 2-category of monads in a 2-category K, by replacing their compatibility constraint of 1-cells with the units of monads by an additional condition on the 2-cells. A relation between monads in EMw(K) and composite pre-monads in K is discussed. If K admits Eilenberg-Moore constructions for monads, we define two symmetrical notions of ‘weak liftings’ for monads in K. If moreover idempotent 2-cells in K split, we describe both kinds of weak lifting via an appropriate pseudo-functor EMw(K)→K. Weak entwining structures and partial entwining structures are shown to realize weak liftings of a comonad for a monad in these respective senses. Weak bialgebras are characterized as algebras and coalgebras, such that the corresponding monads weakly lift for the corresponding comonads and also the comonads weakly lift for the monads. |
| |
Keywords: | 2-Category Monad Weak lifting |
本文献已被 ScienceDirect 等数据库收录! |
|