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In [2], classes of objects injective with respect to a set M of morphisms of a locally presentable category K were characterized: they are precisely the classes closed under products,
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
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
More specifically, a Boolean category should provide the abstract algebraic structure underlying the proofs in Boolean Logic, in the same sense as a Cartesian closed category
As we shall see below, any countable strongly connected category with a terminal object can be fully embedded into Alg(1 × 2) by a functor preserving limits over finitely many
It is convenient to work in a cartesian closed category (e.g. sequential spaces ); this yields nice spaces of measurable functions and nice spaces of measures.. Then σ -additivity
4) In Example 2) replace cat by top and rename objects as points. However, if top is to be understood as the category of all topological spaces then we do not have a functor V
When the including topos is locally connected, we also have the following: L is the smallest subtopos for which (the direct image functor of ) its inclusion preserves S -coproducts,
