Background It seems that the awareness of the self of other individuals developed at first, and then, through-and as as an extension of the others- to oneself, self awareness emerged in a final step. Such pre-historic, societal/social interactions that are based on consensus, are also called `mutual'. These considerations lead to a natural representation of one's `self' emergence in terms of the following mathematical concept.

Definition 0.1   A Rosetta biogroupoid, , is a representation of characteristic, star-connected patterns of two-way social (cooperative) interactions: $\Longleftrightarrow$ , or $\Updownarrow$ , that are defined as topological groupoids with star- ($*$ ), or rose- like, internal symmetries. From a strictly topological viewpoint, a Rosetta biogroupoid is a particular type of highly connected network, or oriented multi-graph, consisting of central nodes (vertices) connected through bi-directional edges representing the mutual interactions between individuals in a population or society; thus, it can also be regarded as a particular type of low-dimensional CW complex with a (CW) cellular structure determined by the organisms, such as humans, and their mutual interactions.

Example An especially interesting case of Rosetta groupoids is that of freely generated structures over a graph, or network, of social interactions with different degrees/orders or levels of connectivities; a good example is that of the Erdös `connectivity' number, defined by the length of the chain connecting an Erdös co-author of a published mathematical paper with Erdös to another co-author of the first one, and so on.

A `Rosetta biogroupoid' structure can be depicted as in the following diagram, but possibly with as many as twenty five branches from the center, reference individual:

(0.1)

Diagram 1: A Rosetta biogroupoid of consensual, societal interactions leading to self-awareness, one's self and full consciousness; there could be as few as five, or as many as twenty five, individuals in a pre-historic society of humans; here only four are represented as branches.

Remark: such cooperative interactions caused- through social and biological coevolution- the emergence of human (and/or `humanoid') structured languages with both syntax and semantics; the latter in their turn facilitated the development of self-awareness and the emergence of the human mind as an ultra-complex system, and consciousness as an ultra-complex (meta-process) of processes.