ɪn mˌæθɪmˈæɾɪks, ɐ kəszˈuːl tˈeɪt ɹˌɛzəlˈuːʃən ɔːɹ kəszˈuːl tˈeɪt kˈɑːmplɛks ʌvðə kwˈoʊʃənt ɹˈɪŋ ˈɑːɹ slˈæʃ ˈɛm ɪz ɐ pɹədʒˈɛktɪv ɹˌɛzəlˈuːʃən ʌv ɪɾ æz ɐn ˈɑːɹmˈɑːdʒuːl wˌɪtʃ ˈɔːlsoʊ hɐz ɐ stɹˈʌktʃɚɹ əvə dˌiːdʒˈiːˈældʒᵻbɹə ˌoʊvɚɹ ˈɑːɹ, wˌɛɹ ˈɑːɹ ɪz ɐ kˈɑːmjuːɾətˌɪv ɹˈɪŋ ænd ˈɛm ˈɑːɹ ɪz ɐn aɪdˈiəl.
In mathematics, a Koszul–Tate resolution or Koszul–Tate complex of the quotient ring R/M is a projective resolution of it as an R-module which also has a structure of a dg-algebra over R, where R is a commutative ring and M ⊂ R is an ideal.