Operad algebra - Operad algebra

Algebrada operad algebra "algebra" dir operad. Bu $ an $ ning umumlashtirilishi assotsiativ algebra komutativ halqa ustida R, operadni almashtirish bilan R.

Ta'riflar

Opera berilgan O (ayt, a nosimmetrik ketma-ketlik a nosimmetrik monoidal b-toifasi C), an opera ustidagi algebra, yoki O-algebra qisqasi, taxminan chap modul tugadi O tomonidan parametrlangan ko'paytmalar bilan O.

Agar O a topologik opera, keyin operada algebra deyish mumkin O-monoid ob'ekt C. Agar C nosimmetrik monoidaldir, bu odatdagi ta'rifni tiklaydi.

Ruxsat bering C kolimitlar bo'yicha taqsimlanadigan monoidal tuzilishga ega bo'lgan nosimmetrik monoidal b-toifali bo'ling. Agar ${ displaystyle f: O dan O '}$ bu operadalar xaritasi va bundan tashqari, agar f homotopiya ekvivalenti, keyin algebralarning g-toifasi tugaydi O yilda C algebralarning ∞-toifasiga tengdir O ' yilda C.^[1]

Shuningdek qarang

• Ring
• Homotopiya Yolg'on algebra

Izohlar

Adabiyotlar

• Jon Frensis, Algebraik geometriya tugadi ${ displaystyle { mathcal {E}} _ {n}}$- uzuklar
• Xinich, Vladimir (1997-02-11). "Gomotopiya algebralarining gomologik algebrasi". arXiv:q-alg / 9702015.

Tashqi havolalar

• http://ncatlab.org/nlab/show/operad
• http://ncatlab.org/nlab/show/algebra+over+an+operad

Bu algebra bilan bog'liq maqola a naycha. Siz Vikipediyaga yordam berishingiz mumkin uni kengaytirish.