Katyayani (कात्यायनी) is an aspect of Mahadevi and the slayer of the tyrannical demon Mahishasura. She is the sixth among the Navadurgas, the nine forms of Hindu goddess Durga who are worshipped during the festival of Navaratri. She is depicted with four, ten or eighteen hands. This is the second name given for Goddess Adi Parashakti in Amarakosha, the Sanskrit lexicon (Goddess Parvati names- Uma, Katyayani, Gauri, Kali, Haimavati, Ishwari).
In Shaktism, she is associated with the fierce forms of Shakti or Durga, a warrior goddess, which also includes Bhadrakali and Chandika, and traditionally she is associated with the colour red, as with Goddess Parvati, the primordial form of Shakti, a fact also mentioned in Patanjali's Mahabhashya on Pāṇini, written in 2nd century BCE.
She is first mentioned in the Taittiriya Aranyaka part of the Yajurveda. Skanda Purana mentions her being created out of the spontaneous anger of Gods, which eventually led to slaying the demon, Mahishasura, mounted on the lion. This occasion is celebrated during the annual Durga Puja festival in most parts of India.
Her exploits are described in the Devi-Bhagavata Purana and Devi Mahatmyam, part of the Markandeya Purana attributed to sage Markandeya Rishi, who wrote it in Sanskrit ca. 400-500 CE. Over a period of time, her presence was also felt in Buddhist and Jain texts and several Tantric text, especially the Kalika Purana(10th century), which mentions Uddiyana or Odradesa (Odisha), as the seat of Goddess Katyayani and Lord Jagannath .
In Hindu traditions like Yoga and Tantra, she is ascribed to the sixth Ajna Chakra or the Third eye chakra and her blessings are invoked by concentrating on this point.
Origin
According to the Vamana Purana she was created from the combined energies of the gods when their anger at the demon Mahishasura manifested itself in the form of energy rays. The rays crystallized in the hermitage of Kātyāyana Rishi, who gave it proper form therefore she is also called Katyayani or "daughter of Katyayana". Elsewhere in texts like Kalika Purana, it is mentioned that it was Rishi Kaytyayana who first worshipped her, hence she came to be known as Katyayani. In either case, she is a demonstration or apparition of the Durga and is worshipped on the sixth day of Navratri festival.
The Vamana Purana mentions the legend of her creation in great detail: "When the gods had sought Vishnu in their distress, he and at his command Shiva, Brahma and the other gods, emitted such flames from their eyes and countenances that a mountain of effulgence was formed, from which became manifest Katyayini, refulgent as a thousand suns, having three eyes, black hair and eighteen arms. Shiva gave her his trident, Vishnu a Sudarshan Chakra or discus, Varuna a shankha, a conch-shell, Agni a dart, Vayu a bow, Surya a quiver full of arrows, Indra a thunderbolt, Kuvera a mace, Brahma a rosary and water-pot, Kala a shield and sword, Visvakarma a battle-axe and other weapons. Thus armed and adored by the gods, Katyayani proceeded to the Mysore hills. There, the asuras saw her and captivated by her beauty they so described her to Mahishasura, their king, that he was anxious to obtain her. On asking for her hand, she told him she must be won in fight. He took on the form of Mahisha, the bull and fought; at length Durga dismounted from her lion, and sprang upon the back of Mahisha, who was in the form of a bull and with her tender feet smote him on the head with such a terrible force that he fell to the ground senseless. Then she cut off his head with her sword and henceforth was called Mahishasuramardini, the Slayer of Mahishasura., The legend also finds mention in Varaha Purana and the classical text of Shaktism, the Devi-Bhagavata Purana Skanda Purana have an other Version, where Katyayani appear as 2 armed Goddess and later Expand Into 12 armed. Here Because of Kartikey's splendor She got her name. Parvati gifts her lion in this Version. Its unique version as Katayayani forgives Mahisha
Other legends
Raktabīja, an aide of Kolhasur, possessed a power (Siddhi) whereby every drop of his blood spilled on earth would give rise to a demon. Due to this power, Bhairava was finding it impossible to kill Raktabīja. Katyayani swallowed all of Raktabīja's blood without letting it fall on earth. She created an Amrut Kunda (tank of nectar) to rejuvenate Bhairava's soldiers, thus playing a crucial role in the war. Her temple to the South of Kolhapur commemorates this.