Factorization systems induced by weak distributive laws
Gabriella B\"ohm
TL;DR
This paper explores the relationship between weak distributive laws in SetMat and pseudoalgebras in Cat, characterizing associated orthogonal factorization systems through a bilinearity property.
Contribution
It establishes a connection between weak distributive laws and pseudoalgebras, providing a new characterization of orthogonal factorization systems.
Findings
Weak distributive laws relate to pseudoalgebras in Cat.
Orthogonal factorization systems are characterized by bilinearity.
The work bridges concepts in SetMat and 2-monad theory.
Abstract
We relate weak distributive laws in SetMat to strictly associative (but not strictly unital) pseudoalgebras of the 2-monad (-)^2 on Cat. The corresponding orthogonal factorization systems are characterized by a certain bilinearity property.
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Taxonomy
TopicsAdvanced Algebra and Logic · Advanced Topics in Algebra · Algebraic structures and combinatorial models