PlanetPhysics/Biogroupoids and Mathematical Models of Species Evolution

Introduction
Biogroupoids, $$\mathcal{G_B}$$, were introduced as mathematical \htmladdnormallink{representations {http://planetphysics.us/encyclopedia/CategoricalGroupRepresentation.html} of evolving biological species} that are defined by (or `consist of') weakly equivalent classes of living organisms, $$E_O$$, specified by inter-breeding organisms;in this case, the weak equivalence relation, $$\sim_w$$, is defined on the set of evolving organisms modeled in terms of functional, isomorphic genome networks, $$G_{iso}^N$$, such as those described by $$LM_n$$-logic networks in \L{}ukasiewicz-Moisil, $$\mathcal{L}M$$ topoi.

AT-Formulation
This biogroupoid concept allows an algebraic topology formulation of the origin of species and biological evolution both at organismal/organismic and biomolecular levels; it represents a new approach to biological evolution from the standpoint of super-complex systems biology.