PlanetPhysics/C 1Category2

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A category $$\mathcal{C}_1$$ with coproducts is called a $$C_1$$-category if for every family of of monomorphisms $$\left\{u_i: A_i \to B_i\right\}$$ the morphism $$\iota := \oplus_i \, u_i: \oplus_i \, A_i \to \oplus_i \, B_i $$ is also a monomorphism.

With certain additional conditions (as explained in ref. ) $$\mathcal{C}_1$$ may satisfy the Grothendieck axiom $$\mathcal{A}b5$$, thus becoming a $$C_3$$-category (Ch. 11 in ).