Cogender

Cogender, or co-gender (from Latin co ("with, together") + gender) is a word that has been used with a few different meanings. It has been coined independently at different times. Cogender can mean:
 * Cogender as a term for gender inclusion: Inclusion of people of different genders in a community, as opposed to a men-only or women-only community. This is the most common way this word is used. When used in print, it's usually in reference to a co-gender school (also called co-education) or to a co-gender LGBT activist group (as opposed to a lesbian-only activist group).
 * Cogender as an umbrella term in anthropology: a term that some anthropologists as a synonym for third gender, that is to say, as an umbrella term for gender variant and LGBT roles and identities in various cultures.
 * Cogender as a gender identity: a specific type of nonbinary identity.

The latter two meanings are explored further below.

In anthropology
Some anthropologists use cogender as a synonym for third gender, that is to say, as an umbrella term for gender variant and LGBT roles and identities in various cultures. Some examples of how anthropologists have used the word "co-gender:"


 * When anthropologists write about shamanic traditions among the indigenous Mapuche (Araucana) people of Chile, they use co-gender to talk about roles that the machi (shamans) take on during their spiritual practice. Historically, as well as today, machi can have had any gender assigned at birth, and their practice involves ritual cross-dressing in order to communicate with certain aspects of their Creator as needed. At different times, they dress to take on a wife role for a male aspect of that deity, or to take on a husband aspect for a female aspect of that deity. The machi becomes part of a male-female pair with the Creator. As concerning "co-gendered identities" of "machi as co-gender specialists",, the machi themselves have often been categorized as Two-Spirit, meaning indigenous gender roles that don't correspond to Western ideas of the strictly cisgender, heterosexual gender binary.
 * Anthropologists writing about cosmologies in which everything is characterized as having female and male aspects have referred to this as a co-gendered cosmos. Based on the primordial male-female deity couple, "in highland Guatemala, husbands and wives are trained together as shamans by a shaman couple. [They are taught to] recognize both cosmic co-gendering and their own co-gendered nature [...] they learn how to properly balance the feminine and masculine dimensions both within their own bodies and the cosmos."

In this capacity, it's far less common for anthropologists to use the term "cogender" than "third gender."

Cogender as a gender identity
A post from August 25th, 2016 titled "Introducing Cogender" on the "Ask A Cogender" blog independently coined another idea of cogender:

cogender (from the latin root co meaning “with, together" and gender) is an inclusive gender identity that is the union of two or more gender identities. A cogender person is ok being identified as any of the genders included in their identity. You can be cogender and not know it if your gender happens to include the sex you were assigned at birth.

The difference between a cogender whose gender happens [to] include the gender they were assigned at birth and cis person is the cogender would ok with being identified as another gender.

one format of expressing this identify is X coY where X and Y are genders. Example girl coboy.

note a cogender person may want parts they don’t have that are associated with their cogenders but don’t need them, this doesn’t mean the don’t experience dysphoria just that they ok with the parts included in their gender identity. Example an agender cogirl person assigned male at birth may feel dysphoria over their genitals (and the reactions there of) and want breasts but don’t need breasts.

In this definition of cogender, it is a specific type of nonbinary and multigender identity.

Cofluid
As coined on the same blog as the above definition of cogender, on August 26, 2016: "cofluid is when one part of the cogender identity is static but the other part(s) change (possibly to match the first part). Example a cofluidboy has a cogender identity that always includes male but the other identities vary."