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In this paper we consider the classification problem of extensions ofYang-Mills-type (YMT) theories. For us, a YMT theory differs from the classicalYang-Mills theories by allowing an arbitrary pairing on the curvature. Thespace of YMT theories with a prescribed gauge group $G$ and instanton sector$P$ is classified, an upper bound to its rank is given and it is compared withthe space of Yang-Mills theories. We present extensions of YMT theories as asimple and unified approach to many different notions of deformations andaddition of correction terms previously discussed in the literature. A relationbetween these extensions and emergence phenomena in the sense ofarXiv:2004.13144 is presented. We consider the space of all extensions of afixed YMT theory $S^G$ and we prove that for every additive group action of$\mathbb{G}$ in $\mathbb{R}$ and every commutative and unital ring $R$, thisspace has an induced structure of $R[\mathbb{G}]$-module bundle. We conjecturethat this bundle can be continuously embedded into a trivial bundle. Morphismsbetween extensions of a fixed YMT theory are defined in such a way that theydefine a category of extensions. It is proved that this category is areflective subcategory of a slice category, reflecting some properties of itslimits and colimits.

On Extensions of Yang-Mills-Type Theories, Their Spaces and Their Categories