1. In the 1960s he wrote fundamental papers on higher homotopy theory and homotopy algebras.

2. A notable use of homotopy is the definition of homotopy groups and cohomotopy groups, important invariants in algebraic topology.

3. It follows that adjoint functors induce homotopy equivalences.

4. It is weakly Contractible if this map is a weak homotopy equivalence, hence if all homotopy groups of X X are trivial

5. Strongly homotopy Lie algebras are associated with manifolds equipped with a closed form.

6. Moreover, a natural transformation between two such functors induces a homotopy between the induced maps.

7. Pretalk Adjunctions and monads Weighted limits Algebras and descent data Monadicity and descent Homotopy coherent Adjunctions A homotopy coherent adjunction in an (1;2)-category K is a simplicial functor Adj !K

8. An equivalent form of the Conjecture involves a coarser form of equivalence than homeomorphism called homotopy equivalence: if a 3-manifold is homotopy equivalent to the 3-sphere, then it is necessarily homeomorphic to it.

9. The deformation of various kinds of mathematical structures can be encapsulated in the language of strongly homotopy Lie algebras.

10. Research involves Multi-disciplinary theoretical and computational research in homotopy theory, the algebra of fitting spaces together.

11. Test sequence

12. Sequence aborted.

13. Paths and loops are central subjects of study in the branch of algebraic topology called homotopy theory.

14. Abort the sequence.

15. Engage landing sequence.

16. unlock sequence aborted.

17. Drift sequence terminated.

18. Initiating communication sequence.

19. Eject sequence initiated.

20. We present Bart, a denoising autoencoder for pretraining sequence-to-sequence models

21. Aborting dialling sequence.

22. Firing sequence aborted.

23. Compressor sequence valve and register charging unit having such compressor sequence valve

24. Create sequence diagram

25. Test conditions and sequence

26. The pulse sequence comprises an acoustic radiation force imaging pulse sequence (500, 600).

27. Dialling sequence aborted, sir.

28. Auto-destruct sequence aborted.

29. Abort auto-destruct sequence.

30. Abort the dialling sequence.

31. Infinity categories (in the form of Joyal's quasi-categories) are a convenient framework to do homotopy theory in abstract settings.

32. Test sequence number five.

33. Self-destruct sequence aborted.

34. Accept guarantee sequence diagram

35. TEST SEQUENCE AND FUEL

36. Sequence of ELR test

37. A sequence of sixes.

38. Along with progress in proving the formality of the strongly homotopy Lie algebras, HQSMCF established close collaborations between leading mathematicians.

39. Abort sequence X-1-X.

40. Method for forwarding an audiovisual sequence, method for receiving said audiovisual sequence, and corresponding system

41. Sergeant, abort the dialling sequence.

42. We re-ran the sequence.

43. (b) Test sequence and cycles

44. Lastly, mathematicians used the theory developed to construct various strongly homotopy Lie algebras as higher central extensions of Lie algebras geometrically.

45. Number the pages in sequence.

46. A first memory stores a sequence of pattern units corresponding to the generated sequence of addresses.

47. Too, some Beziques accept the sequence in any suit, granting 250 points for a sequence in trumps, and 150 points for a sequence in any other suit

48. Expand the Circularize target sequence ()

49. Four minutes to firing sequence.

50. Convergence of Sequence "Does {An^2} Converges => {An} Converges? How to prove it?" Does sequence {An^2} Converges implies to sequence {An} Converges? True or False

51. A sequence of characters is then created from the second bit sequence, where each character in the sequence of characters is represented by an 8-bit combination.

52. Amphibolite facies is usually a product of Barrovian Facies Sequence or advanced Abukuma Facies Sequence metamorphic trajectories

53. Sequence ' ] ] > ' not allowed in content

54. Ranges operate in ASCII collating sequence.

55. Number them in sequence, 3 etc.

56. This maintains the correct patterning sequence.

57. In addition to the spreading sequence, the carrier signal is modulated with a phase reversal sequence (fig.

58. Can't create a sequence step: You can't create a sequence step until you've linked a YouTube channel.

59. That completes the minefield test sequence.

60. Write sequence providing write abort protection

61. These pages are out of sequence.

62. The centromere is difficult to sequence.

63. Method for retrieving sequence-verified nucleic acid fragments and apparatus for amplifying sequence-verified nucleic acid fragments

64. Computer, abort the self-destruct sequence.

65. Pilot-to-pilot connection protocol sequence.

66. Fisher imagined the following evolutionary sequence.

67. It consists of a thick turbidite sequence covered by an interdigitated sequence of lavas and alluvial cone sediments.

68. Alternatively or additionally, measurements can be taken for aligning the actual sequence (A2) to the desired sequence (A1).

69. Your personal encoding sequence is accepted.

70. With the writing of the Alleluia final melismas ( classical sequence ), the history of the sequence begins around 850.

71. And this sequence of neural activation is hypothesized to be the neural basis of those sequence of movements.

72. It often leads to fundamental biological insight into sequence-structure-function relationships of nucleotide or protein sequence families.

73. Genome sequence alignment apparatus and method

74. Unfortunately, the animated sequence is diabolical.

75. Addresses sources of radioactive releases and accident initiators, accident sequence modelling, parameter estimation, accident sequence quantification and documentation.

76. Complementation pairs tend to have higher than average sequence identity/similarity, but sequence identity alone is a poor predictor of replaceability as evidenced by the observations that high sequence similarity does not guarantee replaceability and Complementation pairs can have low sequence similarity

77. This new tool, formulated in terms of homotopy theory, proved to be successful in formulating and solving problems in algebra, particularly in ring theory and module theory.

78. He presented his solution, that amounts in modern terms to a combination of the Durand–Kerner method with the homotopy continuation principle, in 1891.

79. This is not a Collating sequence issue

80. Number of words in a Camelcase sequence