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Accessible set functors are universal

Libor Barto (2019)

Commentationes Mathematicae Universitatis Carolinae

It is shown that every concretizable category can be fully embedded into the category of accessible set functors and natural transformations.

Adjointness between theories and strict theories

Hans-Jürgen Vogel (2003)

Discussiones Mathematicae - General Algebra and Applications

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. If the object class of a dhts-category...

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