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More precisely, the category of bicategories and weak functors is equivalent to the category whose objects are weak 2-categories and whose morphisms are those maps of opetopic
Our definition of entropic category is roughly equivalent to having a single category with two ∗-autonomous structures, one commutative and one cyclic related by a linear
Conversely, a pointed protomodular and regular category satisfies M1.1 (Theorem 12 of [Bourn, 2001]) and the pullback of a cokernel is a cokernel, since they coincide with the
Details are given at the end of this section (see Propo- sition 2.18) after we establish the following characterization of the Kleisli category: a presheaf is free as an algebra for
A right adjoint functor from an exact category in which every object is projective to any category admitting kernel-pairs of split epimorphisms is monadic if and only if it
And people knew quite well that if every object of a “linear category” is equipped with a comonoid structure, and if every map in that category respects the comonoid structure
Thus a further extensive theory arises if we can find, inside a given co-extensive algebraic category, a core variety , meaning a variety whose inclusion has a further right
Every atomic Dedekind category R with relational sums and subobjects is equivalent to a category of matrices over a suitable basis.. This basis is the full proper subcategory induced
