Note on the construction of free monoids
Stephen Lack
TL;DR
This paper presents a method for constructing free monoids within certain monoidal categories that have specific colimit and limit properties, expanding the theoretical framework for algebraic structures in category theory.
Contribution
It introduces a new construction of free monoids in monoidal categories with finite limits and countable colimits, under conditions involving reflexive coequalizers and colimits of chains.
Findings
Constructs free monoids in categories with finite limits and countable colimits.
Shows tensoring preserves reflexive coequalizers and colimits of chains.
Provides a framework for algebraic structures in enriched category theory.
Abstract
We construct free monoids in a monoidal category with finite limits and countable colimits, in which tensoring on either side preserves reflexive coequalizers and colimits of countable chains.
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