Curved homotopy coalgebras
Abstract
We describe the category of homotopy coalgebras, concentrating on properties of relatively cofree homotopy coalgebras, morphisms and coderivations from an ordinary coalgebra to a relatively cofree homotopy coalgebra, morphisms and coderivations between coalgebras of latter type. Cobar- and bar-constructions between counit-complemented curved coalgebras, unit-complemented curved algebras and curved homotopy coalgebras are described. Using twisting cochains an adjunction between cobar- and bar-constructions is derived under additional assumptions.
- Publication:
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arXiv e-prints
- Pub Date:
- February 2014
- DOI:
- 10.48550/arXiv.1402.0408
- arXiv:
- arXiv:1402.0408
- Bibcode:
- 2014arXiv1402.0408L
- Keywords:
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- Mathematics - Category Theory;
- Mathematics - K-Theory and Homology;
- 16T15;
- 18D10;
- 18D15
- E-Print:
- 51 pages