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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...

Cartesian bicategories. II.

Carboni, A., Kelly, G.M., Walters, R.F.C., Wood, R.J. (2007)

Theory and Applications of Categories [electronic only]

Categories of functors between categories with partial morphisms

Hans-Jürgen Vogel (2005)

Discussiones Mathematicae - General Algebra and Applications

It is well-known that the composition of two functors between categories yields a functor again, whenever it exists. The same is true for functors which preserve in a certain sense the structure of symmetric monoidal categories. Considering small symmetric monoidal categories with an additional structure as objects and the structure preserving functors between them as morphisms one obtains different kinds of functor categories, which are even dt-symmetric categories.

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