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ALGEBRAIC CATEGORIES WHOSE PROJECTIVES ARE EXPLICITLY FREE
"... Abstract. Let M = (M, m, u) be a monad and let (MX, m) be the free Malgebra on the object X. Consider an Malgebra (A, a), a retraction r: (MX, m) → (A, a) and a section t: (A, a) → (MX, m) of r. The retract (A, a) is not free in general. We observe that for many monads with a ‘combinatorial flav ..."
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Abstract. Let M = (M, m, u) be a monad and let (MX, m) be the free Malgebra on the object X. Consider an Malgebra (A, a), a retraction r: (MX, m) → (A, a) and a section t: (A, a) → (MX, m) of r. The retract (A, a) is not free in general. We observe that for many monads with a ‘combinatorial flavor ’ such a retract is not only a free algebra (MA0, m), but it is also the case that the object A0 of generators is determined in a canonical way by the section t. We give a precise form of this property, prove a characterization, and discuss examples from combinatorics, universal algebra, convexity and topos theory. 1.
Lagrange’s theorem for Hopf monoids in species
, 2012
"... Abstract. Following Radford’s proof of Lagrange’s theorem for pointed Hopf algebras, ..."
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Abstract. Following Radford’s proof of Lagrange’s theorem for pointed Hopf algebras,
REFLECTIVE KLEISLI SUBCATEGORIES OF THE CATEGORY OF EILENBERGMOORE ALGEBRAS FOR FACTORIZATION MONADS
"... It is well known that for any monad, the associated Kleisli category is embedded in the category of EilenbergMoore algebras as the free ones. We discovered some interesting examples in which this embedding is reflective; that is, it has a left ..."
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It is well known that for any monad, the associated Kleisli category is embedded in the category of EilenbergMoore algebras as the free ones. We discovered some interesting examples in which this embedding is reflective; that is, it has a left