Algebraic & Geometric Topology Volume 22, issue 3 (2022)

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On measurings of algebras over operads and homology theories

Abhishek Banerjee and Surjeet Kour

Algebraic & Geometric Topology 22 (2022) 1113–1158

DOI: 10.2140/agt.2022.22.1113

Bibliography

1	M Anel, Enriching algebras over coalgebras and operads over cooperads, lecture notes (2014)
2	M Anel, A Joyal, Sweedler theory for (co)algebras and the bar-cobar constructions, preprint (2013) arXiv:1309.6952
3	M Barr, Coalgebras over a commutative ring, J. Algebra 32 (1974) 600 MR401881
4	M Batchelor, Difference operators, measuring coalgebras, and quantum group-like objects, Adv. Math. 105 (1994) 190 MR1275664
5	M Batchelor, Measuring comodules: their applications, J. Geom. Phys. 36 (2000) 251 MR1793011
6	H J Baues, E G Minian, B Richter, Crossed modules over operads and operadic cohomology, K–Theory 31 (2004) 39 MR2050878
7	G Böhm, T Brzeziński, R Wisbauer, Monads and comonads on module categories, J. Algebra 322 (2009) 1719 MR2543632
8	F Borceux, Handbook of categorical algebra, II: Categories and structures, 51, Cambridge Univ. Press (1994) MR1313497
9	T Brzeziński, On modules associated to coalgebra Galois extensions, J. Algebra 215 (1999) 290 MR1684158
10	E Dubuc, Adjoint triangles, from: "Reports of the Midwest Category Seminar, II" (editor S Mac Lane), Lecture Notes in Math. 61, Springer (1968) 69 MR0233864
11	B Fresse, Cogroups in algebras over an operad are free algebras, Comment. Math. Helv. 73 (1998) 637 MR1639900
12	B Fresse, Modules over operads and functors, 1967, Springer (2009) MR2494775
13	B Fresse, Homotopy of operads and Grothendieck–Teichmüller groups, I : The algebraic theory and its topological background, 217, Amer. Math. Soc. (2017) MR3643404
14	V Ginzburg, M Kapranov, Koszul duality for operads, Duke Math. J. 76 (1994) 203 MR1301191
15	L Grunenfelder, M Mastnak, On bimeasurings, J. Pure Appl. Algebra 204 (2006) 258 MR2184810
16	L Grunenfelder, M Mastnak, On bimeasurings, II, J. Pure Appl. Algebra 209 (2007) 823 MR2298860
17	V Hinich, V Schechtman, Homotopy Lie algebras, from: "I M Gelfand Seminar" (editors S Gelfand, S Gindikin), Adv. Soviet Math. 16, Amer. Math. Soc. (1993) 1 MR1237833
18	D Husemoller, Lectures on cyclic homology, 83, Springer (1991) MR1162110
19	M Hyland, I López Franco, C Vasilakopoulou, Hopf measuring comonoids and enrichment, Proc. Lond. Math. Soc. 115 (2017) 1118 MR3733560
20	M Hyland, I López Franco, C Vasilakopoulou, Measuring comodules and enrichment, preprint (2017) arXiv:1703.10137
21	G M Kelly, Basic concepts of enriched category theory, 64, Cambridge Univ. Press (1982) 245 MR651714
22	A Lauve, M Mastnak, Bialgebra coverings and transfer of structure, from: "Tensor categories and Hopf algebras" (editors N Andruskiewitsch, D Nikshych), Contemp. Math. 728, Amer. Math. Soc. (2019) 137 MR3943749
23	L Le Bruyn, Universal bialgebras associated with orders, Comm. Algebra 10 (1982) 457 MR647832
24	M Livernet, On a plus-construction for algebras over an operad, K–Theory 18 (1999) 317 MR1738897
25	J L Loday, Cyclic homology, 301, Springer (1992) MR1217970
26	J L Loday, B Vallette, Algebraic operads, 346, Springer (2012) MR2954392
27	S Mac Lane, Categories for the working mathematician, 5, Springer (1971) MR0354798
28	M Markl, Operads and PROPs, from: "Handbook of algebra, V" (editor M Hazewinkel), Elsevier (2008) 87 MR2523450
29	J P May, The geometry of iterated loop spaces, 271, Springer (1972) MR0420610
30	H E Porst, R Street, Generalizations of the Sweedler dual, Appl. Categ. Structures 24 (2016) 619 MR3546505
31	M E Sweedler, Hopf algebras, Benjamin (1969) MR0252485
32	M Takeuchi, Topological coalgebras, J. Algebra 97 (1985) 505 MR813000
33	B Vallette, Homology of generalized partition posets, J. Pure Appl. Algebra 208 (2007) 699 MR2277706
34	C Vasilakopoulou, Enrichment of categories of algebras and modules, preprint (2012) arXiv:1205.6450
35	C Vasilakopoulou, On enriched fibrations, Cah. Topol. Géom. Différ. Catég. 59 (2018) 354 MR3889684
36	C Vasilakopoulou, Enriched duality in double categories : 𝒱–categories and 𝒱–cocategories, J. Pure Appl. Algebra 223 (2019) 2889 MR3912953
37	M B Wischnewsky, On linear representations of affine groups, I, Pacific J. Math. 61 (1975) 551 MR414567