TL;DR
This paper explores the relationship between comonads and functors, detailing how algebras over monads can be enriched over coalgebras via a 2-functor from comonads to functors.
Contribution
It introduces a 2-functor from the 2-category of comonads to functors, elucidating the enrichment of monad algebras over coalgebras.
Findings
Describes properties of the 2-functor from comonads to functors.
Shows how algebras over monads are enriched over coalgebras.
Provides a framework for understanding comonad-related structures.
Abstract
In this article we describe properties of the 2-functor from the 2-category of comonads to the 2-category of functors that sends a comonad to its forgetful functor. This allows us to describe contexts where algebras over a monad are enriched tensored and cotensored over coalgebras over a comonad.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Topics in Algebra