Universal topological algebra needs closed topological categories

DOI10.1016/0166-8641(81)90010-9zbMath0465.18004OpenAlexW2086678978MaRDI QIDQ1154532

Louis D. Nel

Publication date: 1981

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0166-8641(81)90010-9

zbMATH Keywords

categorical tensor product powersclosed topological categorymonoidal closed structurestrongly algebraic categoryuniversal topological algebra

Mathematics Subject Classification ID

Categorical methods in general topology (54B30) Closed categories (closed monoidal and Cartesian closed categories, etc.) (18D15) Algebraic structures (08A99) Categories and theories (18C99)

Related Items (12)

Topological improvements of categories of structured sets ⋮ Optimal subcategories and Stone-Weierstrass ⋮ ESSENTIALLY ALGEBRAIC CATEGORIES ⋮ Topological \(\operatorname{FL}_{\operatorname{ew}}\)-algebras ⋮ EXPONENTIAL LAWS FOR ORDERED “TOPOLOGICAL” VECTOR SPACES ⋮ Free modules over Cartesian closed topological categories ⋮ Topological semi-abelian algebras ⋮ ALGEBRAIC HULLS OF ADJOINT FUNCTORS AS INJECTIVE HULLS ⋮ How Topological are Topological Groups? ⋮ Unnamed Item ⋮ Some weaker versions of topological residuated lattices ⋮ Some topics in topological algebra

Cites Work

• Every topological category is convenient for Gelfand duality
• Monoidal closed, Cartesian closed and convenient categories of topological spaces
• On the categories of general topology and topological algebra
• Colimits of algebras revisited
• CARTESIAN CLOSED COREFLECTIVE HULLS
• On Wyler's Taut lift theorem
• Regular Categories and Regular Functors
• TEN TOPOLOGIES FOR X × Y
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