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We fix any pair $(mathbf{mathscr{C}},mathbf{W})$ consisting of a bicategory and a class of morphisms in it, admitting a bicalculus of fractions, i.e. a localization of $mathbf{mathscr{C}}$ with respect to the class $mathbf{W}$. In the resulting bicategory of fractions, we identify necessary and sufficient conditions for the existence of weak fiber products.
A new categorical framework is provided for dealing with multiple arguments in a programming language with effects, for example in a language with imperative features. Like related frameworks (Monads, Arrows, Freyd categories), we distinguish two kin
We fix any bicategory $mathscr{A}$ together with a class of morphisms $mathbf{W}_{mathscr{A}}$, such that there is a bicategory of fractions $mathscr{A}[mathbf{W}_{mathscr{A}}^{-1}]$. Given another such pair $(mathscr{B},mathbf{W}_{mathscr{B}})$ and
We fix any bicategory $mathscr{A}$ together with a class of morphisms $mathbf{W}_{mathscr{A}}$, such that there is a bicategory of fractions $mathscr{A}[mathbf{W}_{mathscr{A}}^{-1}]$. Given another such pair $(mathscr{B},mathbf{W}_{mathscr{B}})$ and
We define a bicategory in which the 0-cells are the entwinings over variable rings. The 1-cells are triples of a bimodule and two maps of bimodules which satisfy an additional hexagon, two pentagons and two (co)unit triangles; and the 2-cells are the
We give an abstract categorical treatment of Plonka sums and products using lax and oplax morphisms of monads. Plonka sums were originally defined as operations on algebras of regular theories. Their arities are sup-semilattices. It turns out that ev