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Bilinear maps and their classifying tensor products are well-known in the theory of linear algebra, and their generalization to algebras of commutative monads is a classical result of monad theory.
On direct products of theories
Andrzej Mostowski · 1952
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Acyclic models and resolvent functors
Harry Wesley Appelgate · 1965
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The first order properties of products of algebraic systems
Solomon Feferman and Robert L. Vaught · 1967
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Distributive laws
Jon Beck · 1969
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Monads on symmetric monoidal closed categories
Anders Kock · 1970
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Bilinearity and cartesian closed monads
Anders Kock · 1971
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Strong functors and monoidal monads
Anders Kock · 1972
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Adjoint lifting theorems for categories of algebras
Peter T Johnstone · 1975
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Adjunctions and comonads in differential algebra
William Keigher · 1975
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Monadic second-order theories
Yuri Gurevich · 1985
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The monadic second-order logic of graphs. I. Recognizable sets of finite graphs
Bruno Courcelle · 1990
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Graph structure and monadic second-order logic: a language-theoretic approach
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Gavin J Seal · 2013
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The pebbling comonad in finite model theory
Samson Abramsky, Anuj Dawar, and Pengming Wang · 2017
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Categorical Foundations: Special Topics in Order, Topology, Algebra, and Sheaf Theory
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