Geodesic
Adjointness between theories and strict theories
Discussiones Mathematicae. General Algebra and Applications, Tome 23 (2003) no. 2, pp. 163-212

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The categorical concept of a theory for algebras of a given type was foundet by Lawvere in 1963 (see [8]). Hoehnke extended this concept to partial heterogenous algebras in 1976 (see [5]). A partial theory is a dhts-category such that the object class forms a free algebra of type (2,0,0) freely generated by a nonempty set J in the variety determined by the identities ox ≈ o and xo ≈ o, where o and i are the elements selected by the 0-ary operation symbols.
Keywords: symmetric monoidal category, dhts-category, partial theory, adjoint functor 
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Vogel, Hans-Jürgen. Adjointness between theories and strict theories. Discussiones Mathematicae. General Algebra and Applications, Tome 23 (2003) no. 2, pp. 163-212. http://geodesic.mathdoc.fr/item/DMGAA_2003_23_2_a6/