“Krazy Kat,” George Herriman’s exuberant and idiosyncratic newspaper comic, was never broadly popular. From the beginning, though, it found fans among writers and artists. P. G. Wodehouse compared it favorably to Wagner’s “Parsifal”; Jack Kerouac later said it influenced the Beats. The strip ran from 1913 until 1944, the year that Herriman died. It is set in a dreamlike place called Coconino County, where a black cat named Krazy loves a white mouse named Ignatz, who throws bricks at Krazy’s head. Krazy interprets the bricks as “love letters.” Meanwhile, a police-officer dog, Offisa Pup, tries to protect Krazy, with whom he is smitten. The structure of the strip was built on reversals: a cat loves a mouse, a dog protects a feline, and, at a time when anti-miscegenation laws held sway in most of the United States, a black animal yearns for a white one.

That last detail took on additional resonance, in 1971, when Arthur Asa Berger published a story about Herriman’s birth certificate. The certificate described Herriman’s race as “colored,” Berger revealed, to the astonishment of many readers (Ralph Ellison among them). Herriman was born in New Orleans, in 1880, to a mixed-race family; his great-grandfather, Stephen Herriman, was a white New Yorker who had children with a “free woman of color,” Justine Olivier, in what was then a common social arrangement in New Orleans called plaçage. George Herriman was one of the class of Louisianans known as blanc fo’cé_:_ Creoles who actively tried to pass as white. (Creoles who could pass but did not try to were called passé blanc.) In adulthood, Herriman frequently covered his tight curls with a hat, and invented fanciful origin stories that attributed his light brown skin to years living under the sun of Greece. Sometimes he claimed that his ancestors were French or Irish—anything that might sow confusion.

In the years following Berger’s initial reporting, a number of writers have grappled with this aspect of Herriman’s work. “In the comics page no less than in social life, the opposition between black and white can be redefined but not abolished,” the journalist and comics scholar Jeet Heer has written. As Michael Tisserand points out in his new biography, “Krazy,” Herriman might have lost his job as a cartoonist had he been outed as black. When Herriman worked at the Los Angeles Examiner, as a staff artist, the paper published multiple articles about light-skinned African-Americans who had tried to pass as white and were subsequently “exposed.” But “Krazy” also helps to expand the meaning of the comic’s subversive play with identity beyond race. In an era when books depicting homosexuality and gender nonconformity could lead to charges of obscenity, “Krazy Kat,” Tisserand notes, featured a gender-shifting protagonist who was in love with a male character.

Krazy’s gender, to the consternation of many readers, was never stable. Herriman would switch the cat’s pronouns every so often, sometimes within a strip; in one, from 1921, Krazy switches gender four times in a single sentence. When Krazy is portrayed as male, the comic becomes the story of one male character openly pining for another—in some touching scenes, the characters even nestle together to sleep. For all his pestering and punishing of Krazy, Ignatz ultimately seems to have a soft spot for the ingenuous cat; when Krazy plants a kiss on a sleeping Ignatz in one daily, Ignatz’s dreams, suddenly visible to the reader, become filled with little cupids and hearts. In two strips from 1915, Krazy wonders aloud “whether to take unto myself a ‘wife’ or a ‘husband.’ ” In a strip from 1922, an owl attempts to find out Krazy’s gender by knocking on the cat’s door and asking if the lady or gentleman of the house is in, only to find that Krazy answers to both titles. At the end of the exchange, Krazy charmingly self-identifies simply as “me.”

Some fans of “Krazy Kat” were mystified by all of this. In his autobiography, the director Frank Capra described a conversation he had with Herriman on the subject. “I asked him if Krazy Kat was a he or a she,” he writes. Herriman, Capra tells us, lit his pipe before answering. “I get dozens of letters asking me the same question,” Herriman told Capra. “I don’t know. I fooled around with it once; began to think the Kat is a girl—even drew up some strips with her being pregnant. It wasn’t the Kat any longer; too much concerned with her own problems—like a soap opera. . . . Then I realized Krazy was something like a sprite, an elf,” he continued, according to Capra. “They have no sex. So the Kat can’t be a he or a she. The Kat’s a spirit—a pixie—free to butt into anything.” Capra, bemused by the answer, remarked, “If there’s any pixie around here, he’s smoking a pipe.”

In the nineteen-sixties, the American animator Gene Deitch, famed for his work on “Popeye” and other cartoons, was commissioned to adapt “Krazy Kat” for television. But, Tisserand writes, “there was the problem of Krazy Kat’s ambiguous gender.” Deitch himself recalls, “At the time, any hint of a homosexual relationship between Krazy . . . and Ignatz mouse, an obvious male, was a loud no-no. So we declared Krazy a girl cat, and that was that!” (In film adaptations, made decades earlier, Krazy “was cast as a male character and Ignatz, inexplicably, as a black mouse,” Tisserand writes.) Assuming that Krazy was exclusively female was a common response. In a 1946 reflection on the comic, E. E. Cummings acknowledged that Krazy’s gender was fluid, but still identified the feline as female throughout, calling “our heroine” Krazy “the adorably helpless incarnation of saintliness.”

Of course, some readers embraced this aspect of the character. A well-known bohemian bar in Washington, D.C., that welcomed queer customers seemed to acknowledge the strip’s anarchic queerness by naming itself Krazy Kat. (Its sign featured a black cat that resembled Krazy being hit by a brick.) When I corresponded with Tisserand recently, and asked him about the strip’s legacy in this regard, he pointed out that the singer Michael Stipe, of the band R.E.M., who has written about his own fluid sexuality, is one of the strip’s famous fans. (Stipe has two separate “Krazy Kat” tattoos.) In an essay for the Guardian, from 2014, Stipe wrote, “The 21st century has provided all of us, recent generations particularly, with a clearer idea of the breadth of fluidity with which sexuality and identity presents itself in each individual.” In Herriman’s work, Tisserand suggested, Stipe may have found “a beautiful precursor to that idea.”

I asked Tisserand if he thought Herriman’s own experience with racial identity and his depiction of gender in the strip were linked. Tisserand pointed me to a 1914 strip, in which Ignatz asks Krazy about sometimes being a “Miss” and sometimes a “Mr.” “It’s a sed story, ‘Ignatz,’ which will move you to a tear,” Krazy says. “When us ladies first got the ‘votes,’ I went to a voting boot to vote. The man said to me, Is you ‘Miss,’ ‘Mrs.,’ or ‘Mr.’? Not to offend him, I said, Any one which you like sir, or all three should you rather have it that way. Well, it’s here my sedness begun,” Krazy concludes. Tisserand said, “Herriman wouldn’t have had that exact experience, but would have, at the age of nineteen, while living in a boarding house at Coney Island, had to choose his own racial designation, for the first time in his life.” Herriman, like Krazy, might have decided “to choose whatever wouldn’t give offense,” Tisserand proposed. In a world that required rigid demarcations, being someone who didn’t fit neatly could feel both dangerous and demeaning.