Kātyāyanī is the wife of Śiva. In the Radha Tantra, Padminī (Radha) addresses Goddess Katyayani with deep reverence, calling her the “beloved of Śiva.” Later, in the same text, Lord Krishna prays to her for a boon to perfect his spiritual practices, saying, “I bow to you, dear to Śankara” it also notes that in the sacred circle of Mathurā, where Mahāmāyā appears as Goddess Kātyāyanī, she always resides with Śiva.
However, Kātyāyanī is also used for Śrī Lakṣmī.
Mṛtyuñjaya Tantra -
"गोविन्दमहिषीं देवीं कात्यायन्यां भयङ्करीम्,"
which directly translates to "The one who Kātyāyanī is the consort of Govinda".
In the context of Yogamaya, the Sarārthadarśinī commentary by Śrī Viśvanātha Cakravartī explains that the Yogamāyā Devī, worshipped by the gopīs as Katyayani, is Lord Krishna’s own svarūpa-śakti. The commentary uses the term patitvaṁ to indicate her status as a consort of Lord Krishna, affirming that “YogaMāyā Katyāyanī, worshipped by the Gopakaṇyas, is the wife of the Lord.” Additionally, the Brahmāṇḍa Mahāpurāṇa describes Vṛndāvananāyikā Kātyāyanīdevī incarnating as the daughter of Vṛṣabhānu, directly connecting her identity to Radha, Lord Krishna’s eternal beloved.